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<title>Review Exercises and Sample Exam</title>
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<div class="section end-of-chapter" id="fwk-redden-ch05_s08" version="5.0" lang="en">
<h2 class="title editable block">
<span class="title-prefix">5.8</span> Review Exercises and Sample Exam</h2>
<div class="qandaset block" id="fwk-redden-ch05_s08_qs01" defaultlabel="number">
<h3 class="title">Review Exercises</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd01">
<h3 class="title">Roots and Radicals</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd01_qd01">
<p class="para" id="fwk-redden-ch05_s08_qs01_p01"><strong class="emphasis bold">Simplify.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa01">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p02"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2259" display="inline"><mrow><mo>−</mo><msqrt><mrow><mn>121</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa02">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p04"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2260" display="inline"><mrow><msqrt><mrow><msup><mrow><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>7</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa03">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p06"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2261" display="inline"><mrow><msqrt><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mi>y</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa04">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p08"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2263" display="inline"><mrow><msqrt><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>6</mn><mi>x</mi><mo>−</mo><mn>7</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa05">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p10"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2265" display="inline"><mrow><mroot><mrow><mn>125</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa06">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p12"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2266" display="inline"><mrow><mroot><mrow><mtext>−</mtext><mn>27</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa07">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p14"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2267" display="inline"><mrow><mroot><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mi>y</mi></mrow><mo>)</mo></mrow></mrow><mn>3</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa08">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p16"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2269" display="inline"><mrow><mroot><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>3</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa09">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p18">Given <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2271" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msqrt><mrow><mi>x</mi><mo>+</mo><mn>10</mn></mrow></msqrt></mrow></math></span>, find <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2272" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2273" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa10">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p20">Given <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2276" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mroot><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span>, find <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2277" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2278" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mrow><mn>13</mn></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa11">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p22">Determine the domain of the function defined by <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2281" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msqrt><mrow><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow></msqrt></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa12">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p24">Determine the domain of the function defined by <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2283" display="inline"><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mroot><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd01_qd02" start="13">
<p class="para" id="fwk-redden-ch05_s08_qs01_p26"><strong class="emphasis bold">Simplify.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa13">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p27"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2285" display="inline"><mrow><mroot><mrow><mn>250</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa14">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p29"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2287" display="inline"><mrow><mn>4</mn><mroot><mrow><mn>120</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa15">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p31"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2289" display="inline"><mrow><mtext>−</mtext><mn>3</mn><mroot><mrow><mn>108</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa16">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2291" display="block"><mrow><mn>10</mn><mroot><mrow><mfrac><mn>1</mn><mrow><mn>32</mn></mrow></mfrac></mrow><mpadded width="0.6em"><mn>5</mn></mpadded></mroot></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa17">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2292" display="block"><mrow><mtext>−</mtext><mn>6</mn><mroot><mrow><mfrac><mrow><mn>81</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mrow><mpadded width="0.6em"><mn>4</mn></mpadded></mroot></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa18">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p37"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2293" display="inline"><mrow><mroot><mrow><mn>128</mn></mrow><mpadded width="0.4em"><mn>6</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa19">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p39"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2295" display="inline"><mrow><mroot><mrow><mtext>−</mtext><mn>192</mn></mrow><mpadded width="0.4em"><mn>5</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa20">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p41"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2297" display="inline"><mrow><mtext>−</mtext><mn>3</mn><msqrt><mrow><mn>420</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd02">
<h3 class="title">Simplifying Radical Expressions</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd02_qd01" start="21">
<p class="para" id="fwk-redden-ch05_s08_qs01_p43"><strong class="emphasis bold">Simplify.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa21">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p44"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2299" display="inline"><mrow><msqrt><mrow><mn>20</mn><msup><mi>x</mi><mn>4</mn></msup><msup><mi>y</mi><mn>3</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa22">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p46"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2301" display="inline"><mrow><mtext>−</mtext><mn>4</mn><msqrt><mrow><mn>54</mn><msup><mi>x</mi><mn>6</mn></msup><msup><mi>y</mi><mn>3</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa23">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p48"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2303" display="inline"><mrow><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>14</mn><mi>x</mi><mo>+</mo><mn>49</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa24">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p50"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2305" display="inline"><mrow><msqrt><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>8</mn></mrow><mo>)</mo></mrow></mrow><mn>4</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd02_qd02" start="25">
<p class="para" id="fwk-redden-ch05_s08_qs01_p52"><strong class="emphasis bold">Simplify. (Assume all variable expressions are nonzero.)</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa25">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p53"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2307" display="inline"><mrow><msqrt><mrow><mn>100</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>4</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa26">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p55"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2309" display="inline"><mrow><msqrt><mrow><mn>36</mn><msup><mi>a</mi><mn>6</mn></msup><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa27">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2311" display="block"><mrow><msqrt><mrow><mfrac><mrow><mn>8</mn><msup><mi>a</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>4</mn></msup></mrow></mfrac></mrow></msqrt></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa28">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2313" display="block"><mrow><msqrt><mrow><mfrac><mrow><mn>72</mn><msup><mi>x</mi><mn>4</mn></msup><mi>y</mi></mrow><mrow><msup><mi>z</mi><mn>6</mn></msup></mrow></mfrac></mrow></msqrt></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa29">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p61"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2315" display="inline"><mrow><mn>10</mn><mi>x</mi><msqrt><mrow><mn>150</mn><msup><mi>x</mi><mn>7</mn></msup><msup><mi>y</mi><mn>4</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa30">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p63"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2317" display="inline"><mrow><mtext>−</mtext><mn>5</mn><msup><mi>n</mi><mn>2</mn></msup><msqrt><mrow><mn>25</mn><msup><mi>m</mi><mrow><mn>10</mn></mrow></msup><msup><mi>n</mi><mn>6</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa31">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p65"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2319" display="inline"><mrow><mroot><mrow><mn>48</mn><msup><mi>x</mi><mn>6</mn></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa32">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p67"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2321" display="inline"><mrow><mroot><mrow><mn>270</mn><msup><mi>a</mi><mrow><mn>10</mn></mrow></msup><msup><mi>b</mi><mn>8</mn></msup><msup><mi>c</mi><mn>3</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa33">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2323" display="block"><mrow><mroot><mrow><mfrac><mrow><msup><mi>a</mi><mn>3</mn></msup><msup><mi>b</mi><mn>5</mn></msup></mrow><mrow><mn>64</mn><msup><mi>c</mi><mn>6</mn></msup></mrow></mfrac></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa34">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2325" display="block"><mrow><mroot><mrow><mfrac><mrow><msup><mi>a</mi><mrow><mn>26</mn></mrow></msup></mrow><mrow><mn>32</mn><msup><mi>b</mi><mn>5</mn></msup><msup><mi>c</mi><mrow><mn>10</mn></mrow></msup></mrow></mfrac></mrow><mpadded width="0.4em"><mn>5</mn></mpadded></mroot></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa35">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p73">The period <em class="emphasis">T</em> in seconds of a pendulum is given by the formula <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2327" display="inline"><mrow><mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><msqrt><mrow><mfrac><mi>L</mi><mrow><mn>32</mn></mrow></mfrac></mrow></msqrt></mrow></math></span> where <em class="emphasis">L</em> represents the length in feet of the pendulum. Calculate the period of a pendulum that is <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2328" display="inline"><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span> feet long. Give the exact answer and the approximate answer to the nearest hundredth of a second.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa36">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p75">The time in seconds an object is in free fall is given by the formula <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2330" display="inline"><mrow><mi>t</mi><mo>=</mo><mfrac><mrow><msqrt><mi>s</mi></msqrt></mrow><mn>4</mn></mfrac></mrow></math></span> where <em class="emphasis">s</em> represents the distance in feet the object has fallen. How long does it take an object to fall 28 feet? Give the exact answer and the approximate answer to the nearest tenth of a second.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa37">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p77">Find the distance between (−5, 6) and (−3,−4).</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa38">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p79">Find the distance between <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2333" display="inline"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>,</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>)</mo></mrow></mrow></math></span> and <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2334" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mo>−</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd02_qd03" start="39">
<p class="para" id="fwk-redden-ch05_s08_qs01_p81"><strong class="emphasis bold">Determine whether or not the three points form a right triangle. Use the Pythagorean theorem to justify your answer.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa39">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p82">(−4,5), (−3,−1), and (3,0)</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa40">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p84">(−1,−1), (1,3), and (−6,1)</p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd03">
<h3 class="title">Adding and Subtracting Radical Expressions</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd03_qd01" start="41">
<p class="para" id="fwk-redden-ch05_s08_qs01_p86"><strong class="emphasis bold">Simplify. Assume all radicands containing variables are nonnegative.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa41">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p87"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2336" display="inline"><mrow><mn>7</mn><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>5</mn><msqrt><mn>2</mn></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa42">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p89"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2338" display="inline"><mrow><mn>8</mn><msqrt><mrow><mn>15</mn></mrow></msqrt><mo>−</mo><mn>2</mn><msqrt><mrow><mn>15</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa43">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p91"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2340" display="inline"><mrow><mn>14</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>5</mn><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>6</mn><msqrt><mn>2</mn></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa44">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p93"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2342" display="inline"><mrow><mn>22</mn><msqrt><mrow><mi>a</mi><mi>b</mi></mrow></msqrt><mo>−</mo><mn>5</mn><mi>a</mi><msqrt><mi>b</mi></msqrt><mo>+</mo><mn>7</mn><msqrt><mrow><mi>a</mi><mi>b</mi></mrow></msqrt><mo>−</mo><mn>2</mn><mi>a</mi><msqrt><mi>b</mi></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa45">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p95"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2344" display="inline"><mrow><mn>7</mn><msqrt><mi>x</mi></msqrt><mo>−</mo><mrow><mo>(</mo><mrow><mn>3</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>y</mi></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa46">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p97"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2346" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>8</mn><mi>y</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>7</mn><mi>x</mi><msqrt><mi>y</mi></msqrt></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><mn>5</mn><mi>x</mi><msqrt><mi>y</mi></msqrt><mo>−</mo><mn>12</mn><mi>y</mi><msqrt><mi>x</mi></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa47">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p99"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2348" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>6</mn></msqrt></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mn>8</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>6</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa48">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p101"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2350" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>4</mn><mroot><mn>3</mn><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mroot><mrow><mn>12</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><mn>5</mn><mroot><mn>3</mn><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mn>2</mn><mroot><mrow><mn>12</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa49">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p103"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2352" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mo>−</mo><msqrt><mrow><mn>10</mn><mi>x</mi></mrow></msqrt><mo>+</mo><mn>3</mn><msqrt><mi>y</mi></msqrt></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mn>2</mn><msqrt><mrow><mn>10</mn><mi>x</mi></mrow></msqrt><mo>−</mo><mn>6</mn><msqrt><mi>y</mi></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa50">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2354" display="block"><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mi>a</mi><mroot><mrow><mi>a</mi><msup><mi>b</mi><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mn>6</mn><mroot><mrow><msup><mi>a</mi><mn>2</mn></msup><mi>b</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mn>9</mn><mi>a</mi><mroot><mrow><mi>a</mi><msup><mi>b</mi><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mn>12</mn><mroot><mrow><msup><mi>a</mi><mn>2</mn></msup><mi>b</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow><mo>)</mo></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa51">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p107"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2356" display="inline"><mrow><msqrt><mrow><mn>45</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>12</mn></mrow></msqrt><mo>−</mo><msqrt><mrow><mn>20</mn></mrow></msqrt><mo>−</mo><msqrt><mrow><mn>75</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa52">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p109"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2358" display="inline"><mrow><msqrt><mrow><mn>24</mn></mrow></msqrt><mo>−</mo><msqrt><mrow><mn>32</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>54</mn></mrow></msqrt><mo>−</mo><mn>2</mn><msqrt><mrow><mn>32</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa53">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p111"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2360" display="inline"><mrow><mn>2</mn><msqrt><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>45</mn><mi>x</mi></mrow></msqrt><mo>−</mo><mi>x</mi><msqrt><mrow><mn>27</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>20</mn><mi>x</mi></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa54">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p113"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2362" display="inline"><mrow><mn>5</mn><msqrt><mrow><mn>6</mn><msup><mi>a</mi><mn>2</mn></msup><mi>b</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mn>8</mn><msup><mi>a</mi><mn>2</mn></msup><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt><mo>−</mo><mn>2</mn><msqrt><mrow><mn>24</mn><msup><mi>a</mi><mn>2</mn></msup><mi>b</mi></mrow></msqrt><mo>−</mo><mi>a</mi><msqrt><mrow><mn>18</mn><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa55">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p115"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2364" display="inline"><mrow><mn>5</mn><mi>y</mi><msqrt><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mi>y</mi></mrow></msqrt><mo>−</mo><mrow><mo>(</mo><mrow><mi>x</mi><msqrt><mrow><mn>16</mn><msup><mi>y</mi><mn>3</mn></msup></mrow></msqrt><mo>−</mo><mn>2</mn><msqrt><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>3</mn></msup></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa56">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p117"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2366" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mi>b</mi><msqrt><mrow><mn>9</mn><msup><mi>a</mi><mn>2</mn></msup><mi>c</mi></mrow></msqrt><mo>−</mo><mn>3</mn><mi>a</mi><msqrt><mrow><mn>16</mn><msup><mi>b</mi><mn>2</mn></msup><mi>c</mi></mrow></msqrt></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><msqrt><mrow><mn>64</mn><msup><mi>a</mi><mn>2</mn></msup><msup><mi>b</mi><mn>2</mn></msup><mi>c</mi></mrow></msqrt><mo>−</mo><mn>9</mn><mi>b</mi><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mi>c</mi></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa57">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p119"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2368" display="inline"><mrow><mroot><mrow><mn>216</mn><mi>x</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mroot><mrow><mn>125</mn><mi>x</mi><mi>y</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mroot><mrow><mn>8</mn><mi>x</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa58">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p121"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2370" display="inline"><mrow><mroot><mrow><mn>128</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mn>2</mn><mi>x</mi><mroot><mrow><mn>54</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mn>3</mn><mroot><mrow><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa59">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p123"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2372" display="inline"><mrow><mroot><mrow><mn>8</mn><msup><mi>x</mi><mn>3</mn></msup><mi>y</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mn>2</mn><mi>x</mi><mroot><mrow><mn>8</mn><mi>y</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mroot><mrow><mn>27</mn><msup><mi>x</mi><mn>3</mn></msup><mi>y</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mi>x</mi><mroot><mi>y</mi><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa60">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p125"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2374" display="inline"><mrow><mroot><mrow><mn>27</mn><msup><mi>a</mi><mn>3</mn></msup><mi>b</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mn>3</mn><mroot><mrow><mn>8</mn><mi>a</mi><msup><mi>b</mi><mn>3</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mi>a</mi><mroot><mrow><mn>64</mn><mi>b</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mi>b</mi><mroot><mi>a</mi><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa61">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p127">Calculate the perimeter of the triangle formed by the following set of vertices: <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2376" display="inline"><mrow><mrow><mo>{</mo><mrow><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>3</mn><mo>,</mo><mtext>−</mtext><mn>2</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>1</mn><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mtext>−</mtext><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mo>}</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa62">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p129">Calculate the perimeter of the triangle formed by the following set of vertices: <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2378" display="inline"><mrow><mrow><mo>{</mo><mrow><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mtext>−</mtext><mn>4</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>3</mn><mo>,</mo><mn>0</mn></mrow><mo>)</mo></mrow></mrow><mo>}</mo></mrow></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd04">
<h3 class="title">Multiplying and Dividing Radical Expressions</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd04_qd01" start="63">
<p class="para" id="fwk-redden-ch05_s08_qs01_p131"><strong class="emphasis bold">Multiply.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa63">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p132"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2380" display="inline"><mrow><msqrt><mn>6</mn></msqrt><mo>⋅</mo><msqrt><mrow><mn>15</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa64">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p134"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2382" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>4</mn><msqrt><mn>2</mn></msqrt></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa65">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p136"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2383" display="inline"><mrow><msqrt><mn>2</mn></msqrt><mrow><mo>(</mo><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mrow><mn>10</mn></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa66">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p138"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2385" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa67">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p140"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2387" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>5</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>5</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa68">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p142"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2388" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>5</mn><msqrt><mn>3</mn></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa69">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p144"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2390" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>5</mn><msqrt><mi>b</mi></msqrt></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa70">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p146"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2392" display="inline"><mrow><mn>3</mn><msqrt><mrow><mi>x</mi><mi>y</mi></mrow></msqrt><mrow><mo>(</mo><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>2</mn><msqrt><mi>y</mi></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa71">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p148"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2394" display="inline"><mrow><mroot><mrow><mn>3</mn><msup><mi>a</mi><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>⋅</mo><mroot><mrow><mn>18</mn><mi>a</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa72">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p150"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2396" display="inline"><mrow><mroot><mrow><mn>49</mn><msup><mi>a</mi><mn>2</mn></msup><mi>b</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>⋅</mo><mroot><mrow><mn>7</mn><msup><mi>a</mi><mn>2</mn></msup><msup><mi>b</mi><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd04_qd02" start="73">
<p class="para" id="fwk-redden-ch05_s08_qs01_p152"><strong class="emphasis bold">Divide. Assume all variables represent nonzero numbers and rationalize the denominator where appropriate.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa73">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2398" display="block"><mrow><mfrac><mrow><msqrt><mrow><mn>72</mn></mrow></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mn>9</mn></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa74">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2400" display="block"><mrow><mfrac><mrow><mn>10</mn><msqrt><mrow><mn>48</mn></mrow></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mrow><mn>64</mn></mrow></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa75">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2402" display="block"><mrow><mfrac><mn>5</mn><mrow><mpadded height="1.4em"><msqrt><mn>5</mn></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa76">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2404" display="block"><mrow><mfrac><mrow><msqrt><mrow><mn>15</mn></mrow></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mn>2</mn></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa77">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2406" display="block"><mrow><mfrac><mn>3</mn><mrow><mn>2</mn><mpadded height="1.5em"><msqrt><mn>6</mn></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa78">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2408" display="block"><mrow><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mrow><mn>10</mn></mrow></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa79">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2410" display="block"><mrow><mfrac><mrow><mn>18</mn></mrow><mrow><mpadded height="1.4em"><msqrt><mrow><mn>3</mn><mi>x</mi></mrow></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa80">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2412" display="block"><mrow><mfrac><mrow><mn>2</mn><msqrt><mrow><mn>3</mn><mi>x</mi></mrow></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mrow><mn>6</mn><mi>x</mi><mi>y</mi></mrow></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa81">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2414" display="block"><mrow><mfrac><mn>1</mn><mrow><mroot><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mpadded width="0.6em"><mn>3</mn></mpadded></mroot></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa82">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2416" display="block"><mrow><mfrac><mrow><mn>5</mn><mi>a</mi><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mroot><mrow><mn>5</mn><msup><mi>a</mi><mn>2</mn></msup><mi>b</mi></mrow><mpadded width="0.6em"><mn>3</mn></mpadded></mroot></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa83">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2418" display="block"><mrow><mroot><mrow><mfrac><mrow><mn>5</mn><mi>x</mi><msup><mi>z</mi><mn>2</mn></msup></mrow><mrow><mn>49</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mi>z</mi></mrow></mfrac></mrow><mpadded width="0.6em"><mn>3</mn></mpadded></mroot></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa84">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2420" display="block"><mrow><mfrac><mn>1</mn><mrow><mroot><mrow><mn>8</mn><msup><mi>x</mi><mn>4</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mi>z</mi></mrow><mpadded width="0.6em"><mn>5</mn></mpadded></mroot></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa85">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2422" display="block"><mrow><mfrac><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mi>y</mi></mrow><mrow><mroot><mrow><mn>81</mn><mi>x</mi><msup><mi>y</mi><mn>2</mn></msup><msup><mi>z</mi><mn>3</mn></msup></mrow><mpadded width="0.6em"><mn>5</mn></mpadded></mroot></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa86">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2424" display="block"><mrow><mroot><mrow><mfrac><mrow><mn>27</mn><mi>a</mi><msup><mi>b</mi><mn>3</mn></msup></mrow><mrow><mn>15</mn><msup><mi>a</mi><mn>4</mn></msup><mi>b</mi><msup><mi>c</mi><mn>2</mn></msup></mrow></mfrac></mrow><mpadded width="0.6em"><mn>5</mn></mpadded></mroot></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa87">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2426" display="block"><mrow><mfrac><mn>1</mn><mrow><mpadded height="1.4em"><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa88">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2428" display="block"><mrow><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mn>2</mn></msqrt></mpadded><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa89">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2430" display="block"><mrow><mfrac><mrow><mtext>−</mtext><mn>3</mn><msqrt><mn>6</mn></msqrt></mrow><mrow><mn>2</mn><mo>−</mo><mpadded height="1.5em"><msqrt><mrow><mn>10</mn></mrow></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa90">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2432" display="block"><mrow><mfrac><mrow><msqrt><mrow><mi>x</mi><mi>y</mi></mrow></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa91">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2434" display="block"><mrow><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>6</mn></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa92">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2436" display="block"><mrow><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><mpadded height="1.4em"><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mpadded></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa93">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p193">The base of a triangle measures <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2438" display="inline"><mrow><mn>2</mn><msqrt><mn>6</mn></msqrt></mrow></math></span> units and the height measures <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2439" display="inline"><mrow><mn>3</mn><msqrt><mrow><mn>15</mn></mrow></msqrt></mrow></math></span> units. Find the area of the triangle.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa94">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p195">If each side of a square measures <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2441" display="inline"><mrow><mn>5</mn><mo>+</mo><mn>2</mn><msqrt><mrow><mn>10</mn></mrow></msqrt></mrow></math></span> units, find the area of the square.</p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd05">
<h3 class="title">Rational Exponents</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd05_qd01" start="95">
<p class="para" id="fwk-redden-ch05_s08_qs01_p197"><strong class="emphasis bold">Express in radical form.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa95">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p198"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2443" display="inline"><mrow><msup><mrow><mn>11</mn></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa96">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p200"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2445" display="inline"><mrow><msup><mn>2</mn><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa97">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p202"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2447" display="inline"><mrow><msup><mi>x</mi><mrow><mn>3</mn><mo>/</mo><mn>5</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa98">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p204"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2449" display="inline"><mrow><msup><mi>a</mi><mrow><mtext>−</mtext><mn>4</mn><mo>/</mo><mn>5</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd05_qd02" start="99">
<p class="para" id="fwk-redden-ch05_s08_qs01_p206"><strong class="emphasis bold">Write as a radical and then simplify.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa99">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p207"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2451" display="inline"><mrow><msup><mrow><mn>16</mn></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa100">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p209"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2452" display="inline"><mrow><msup><mrow><mn>72</mn></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa101">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p211"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2454" display="inline"><mrow><msup><mn>8</mn><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa102">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p213"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2456" display="inline"><mrow><msup><mrow><mn>32</mn></mrow><mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa103">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2458" display="block"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>9</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa104">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2459" display="block"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mrow><mn>216</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mtext>−</mtext><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd05_qd03" start="105">
<p class="para" id="fwk-redden-ch05_s08_qs01_p219"><strong class="emphasis bold">Perform the operations and simplify. Leave answers in exponential form.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa105">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p220"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2460" display="inline"><mrow><msup><mn>6</mn><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>⋅</mo><msup><mn>6</mn><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa106">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p222"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2461" display="inline"><mrow><msup><mn>3</mn><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>⋅</mo><msup><mn>3</mn><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa107">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2463" display="block"><mrow><mfrac><mrow><msup><mn>6</mn><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow><mrow><msup><mn>6</mn><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa108">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2464" display="block"><mrow><mfrac><mrow><msup><mn>4</mn><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup></mrow><mrow><msup><mn>4</mn><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa109">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p228"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2465" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>64</mn><msup><mi>x</mi><mn>6</mn></msup><msup><mi>y</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa110">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p230"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2467" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>27</mn><msup><mi>x</mi><mrow><mn>12</mn></mrow></msup><msup><mi>y</mi><mn>6</mn></msup></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa111">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2469" display="block"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><msup><mi>a</mi><mrow><mn>4</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow><mrow><msup><mi>a</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn><mo>/</mo><mn>5</mn></mrow></msup></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa112">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2471" display="block"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mrow><mn>4</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa113">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2473" display="block"><mrow><mfrac><mrow><mn>56</mn><msup><mi>x</mi><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup><msup><mi>y</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow><mrow><mn>14</mn><msup><mi>x</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mi>y</mi><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa114">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2475" display="block"><mrow><mfrac><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>4</mn><msup><mi>a</mi><mn>4</mn></msup><msup><mi>b</mi><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup><msup><mi>c</mi><mrow><mn>4</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><msup><mi>b</mi><mrow><mn>1</mn><mo>/</mo><mn>6</mn></mrow></msup><msup><mi>c</mi><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa115">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p240"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2477" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>9</mn><msup><mi>x</mi><mrow><mtext>−</mtext><mn>4</mn><mo>/</mo><mn>3</mn></mrow></msup><msup><mi>y</mi><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow><mtext>−</mtext><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa116">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p242"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2479" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>16</mn><msup><mi>x</mi><mrow><mtext>−</mtext><mn>4</mn><mo>/</mo><mn>5</mn></mrow></msup><msup><mi>y</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><msup><mi>z</mi><mrow><mtext>−</mtext><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow><mtext>−</mtext><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd05_qd04" start="117">
<p class="para" id="fwk-redden-ch05_s08_qs01_p244"><strong class="emphasis bold">Perform the operations with mixed indices.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa117">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p245"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2481" display="inline"><mrow><msqrt><mi>y</mi></msqrt><mo>⋅</mo><mroot><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>5</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa118">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p247"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2483" display="inline"><mrow><mroot><mi>y</mi><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>⋅</mo><mroot><mrow><msup><mi>y</mi><mn>3</mn></msup></mrow><mpadded width="0.4em"><mn>5</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa119">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p249"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2485" display="inline"><mrow><mfrac><mrow><mroot><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mpadded width="0.65em"><mn>3</mn></mpadded></mroot></mrow><mrow><mroot><mi>y</mi><mpadded width="0.6em"><mn>5</mn></mpadded></mroot></mrow></mfrac></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa120">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p251"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2487" display="inline"><mrow><msqrt><mrow><mroot><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></msqrt></mrow></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd06">
<h3 class="title">Solving Radical Equations</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd06_qd01" start="121">
<p class="para" id="fwk-redden-ch05_s08_qs01_p253"><strong class="emphasis bold">Solve.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa121">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p254"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2489" display="inline"><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>3</mn><mo>=</mo><mn>13</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa122">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p256"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2490" display="inline"><mrow><msqrt><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>2</mn></mrow></msqrt><mo>=</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa123">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p258"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2491" display="inline"><mrow><msqrt><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow></msqrt><mo>+</mo><mn>4</mn><mo>=</mo><mn>8</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa124">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p260"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2492" display="inline"><mrow><mn>5</mn><msqrt><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>+</mo><mn>7</mn><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa125">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p262"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2493" display="inline"><mrow><msqrt><mrow><mn>4</mn><mi>x</mi><mo>−</mo><mn>3</mn></mrow></msqrt><mo>=</mo><msqrt><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>15</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa126">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p264"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2494" display="inline"><mrow><msqrt><mrow><mn>8</mn><mi>x</mi><mo>−</mo><mn>15</mn></mrow></msqrt><mo>=</mo><mi>x</mi></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa127">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p266"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2495" display="inline"><mrow><mi>x</mi><mo>−</mo><mn>1</mn><mo>=</mo><msqrt><mrow><mn>13</mn><mo>−</mo><mi>x</mi></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa128">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p268"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2496" display="inline"><mrow><msqrt><mrow><mn>4</mn><mi>x</mi><mo>−</mo><mn>3</mn></mrow></msqrt><mo>=</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>3</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa129">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p270"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2497" display="inline"><mrow><msqrt><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msqrt><mo>=</mo><mn>5</mn><mo>−</mo><msqrt><mi>x</mi></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa130">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p272"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2498" display="inline"><mrow><msqrt><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></msqrt><mo>=</mo><mn>3</mn><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa131">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p274"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2499" display="inline"><mrow><msqrt><mrow><mn>2</mn><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></msqrt><mo>−</mo><msqrt><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></msqrt><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa132">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p276"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2500" display="inline"><mrow><msqrt><mrow><mn>6</mn><mo>−</mo><mi>x</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow></msqrt><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa133">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p278"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2501" display="inline"><mrow><msqrt><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>2</mn></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></msqrt><mo>=</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa134">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p280"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2502" display="inline"><mrow><msqrt><mrow><mn>9</mn><mo>−</mo><mi>x</mi></mrow></msqrt><mo>=</mo><msqrt><mrow><mi>x</mi><mo>+</mo><mn>16</mn></mrow></msqrt><mo>−</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa135">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p282"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2503" display="inline"><mrow><mroot><mrow><mn>4</mn><mi>x</mi><mo>−</mo><mn>3</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa136">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p284"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2505" display="inline"><mrow><mroot><mrow><mi>x</mi><mo>−</mo><mn>8</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>=</mo><mtext>−</mtext><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa137">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p286"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2506" display="inline"><mrow><mroot><mrow><mi>x</mi><mrow><mo>(</mo><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mo>)</mo></mrow></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa138">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p288"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2508" display="inline"><mrow><mroot><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mn>4</mn><mo>=</mo><mn>5</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa139">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p290"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2510" display="inline"><mrow><mroot><mrow><mn>3</mn><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>=</mo><mroot><mrow><mn>5</mn><mi>x</mi><mo>+</mo><mn>37</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa140">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p292"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2512" display="inline"><mrow><mroot><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>9</mn><mi>x</mi><mo>+</mo><mn>24</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>=</mo><mroot><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa141">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p294"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2514" display="inline"><mrow><msup><mi>y</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>−</mo><mn>3</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa142">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p296"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2515" display="inline"><mrow><msup><mi>y</mi><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa143">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p298"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2516" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>−</mo><mn>2</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa144">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p300"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2517" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>−</mo><mn>5</mn><mo>=</mo><mn>0</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa145">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p302"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2518" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>=</mo><msup><mi>x</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa146">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p304"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2519" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></mrow></msup><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></mrow></msup><mo>=</mo><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa147">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p306"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2520" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mi>x</mi></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>=</mo><mtext>−</mtext><mn>2</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa148">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p308"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2521" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>5</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>=</mo><mn>3</mn><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa149">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p310">Solve for <em class="emphasis">g</em>: <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2523" display="inline"><mrow><mi>t</mi><mo>=</mo><msqrt><mrow><mfrac><mrow><mn>2</mn><mi>s</mi></mrow><mi>g</mi></mfrac></mrow></msqrt></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa150">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p312">Solve for <em class="emphasis">x</em>: <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2525" display="inline"><mrow><mi>y</mi><mo>=</mo><mroot><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>−</mo><mn>2</mn></mrow><mo>.</mo></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa151">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p314">The period in seconds of a pendulum is given by the formula <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2527" display="inline"><mrow><mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><msqrt><mrow><mfrac><mi>L</mi><mrow><mn>32</mn></mrow></mfrac></mrow></msqrt></mrow></math></span> where <em class="emphasis">L</em> represents the length in feet of the pendulum. Find the length of a pendulum that has a period of <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2528" display="inline"><mrow><mn>1</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span> seconds. Find the exact answer and the approximate answer rounded off to the nearest tenth of a foot.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa152">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p316">The outer radius of a spherical shell is given by the formula <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2530" display="inline"><mrow><mi>r</mi><mo>=</mo><mroot><mrow><mfrac><mrow><mn>3</mn><mi>V</mi></mrow><mrow><mn>4</mn><mi>π</mi></mrow></mfrac></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mn>2</mn></mrow></math></span> where <em class="emphasis">V</em> represents the inner volume in cubic centimeters. If the outer radius measures 8 centimeters, find the inner volume of the sphere.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa153">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p318">The speed of a vehicle before the brakes are applied can be estimated by the length of the skid marks left on the road. On dry pavement, the speed <em class="emphasis">v</em> in miles per hour can be estimated by the formula <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2532" display="inline"><mrow><mi>v</mi><mo>=</mo><mn>2</mn><msqrt><mrow><mn>6</mn><mi>d</mi></mrow></msqrt></mrow></math></span>, where <em class="emphasis">d</em> represents the length of the skid marks in feet. Estimate the length of a skid mark if the vehicle is traveling 30 miles per hour before the brakes are applied.</p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa154">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p320">Find the real root of the function defined by <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2533" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mroot><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow><mpadded width="0.4em"><mn>3</mn></mpadded></mroot><mo>+</mo><mn>2</mn></mrow><mo>.</mo></math></span></p>
</div>
</li>
</ol>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd07">
<h3 class="title">Complex Numbers and Their Operations</h3>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd07_qd01" start="155">
<p class="para" id="fwk-redden-ch05_s08_qs01_p322"><strong class="emphasis bold">Write the complex number in standard form</strong> <span class="inlineequation"><math xml:id="fwk-redden-ch05_m2534" display="inline"><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mi>i</mi></mrow><mo>.</mo></math></span></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa155">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p323"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2535" display="inline"><mrow><mn>5</mn><mo>−</mo><msqrt><mrow><mtext>−</mtext><mn>16</mn></mrow></msqrt></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa156">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p325"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2537" display="inline"><mrow><mo>−</mo><msqrt><mrow><mtext>−</mtext><mn>25</mn></mrow></msqrt><mo>−</mo><mn>6</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa157">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2539" display="block"><mrow><mfrac><mrow><mn>3</mn><mo>+</mo><msqrt><mrow><mtext>−</mtext><mn>8</mn></mrow></msqrt></mrow><mrow><mn>10</mn></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa158">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2541" display="block"><mrow><mfrac><mrow><msqrt><mrow><mtext>−</mtext><mn>12</mn></mrow></msqrt><mo>−</mo><mn>4</mn></mrow><mn>6</mn></mfrac></mrow></math></span>
</div>
</li>
</ol>
<ol class="qandadiv" id="fwk-redden-ch05_s08_qs01_qd07_qd02" start="159">
<p class="para" id="fwk-redden-ch05_s08_qs01_p331"><strong class="emphasis bold">Perform the operations.</strong></p>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa159">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p332"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2543" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>6</mn><mo>−</mo><mn>12</mn><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mn>4</mn><mo>+</mo><mn>7</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa160">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p334"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2545" display="inline"><mrow><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>3</mn><mo>+</mo><mn>2</mn><mi>i</mi></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><mn>6</mn><mo>−</mo><mn>4</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa161">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2547" display="block"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>−</mo><mi>i</mi></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>−</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa162">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2549" display="block"><mrow><mrow><mo>(</mo><mrow><mfrac><mn>5</mn><mn>8</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa163">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p340"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2551" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>5</mn><mo>−</mo><mn>2</mn><mi>i</mi></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><mn>6</mn><mo>−</mo><mn>7</mn><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mn>4</mn><mo>−</mo><mn>4</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa164">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p342"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2553" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>10</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mn>20</mn><mo>+</mo><mn>5</mn><mi>i</mi></mrow><mo>)</mo></mrow><mo>−</mo><mrow><mo>(</mo><mrow><mn>30</mn><mo>−</mo><mn>15</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa165">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p344"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2555" display="inline"><mrow><mn>4</mn><mi>i</mi><mrow><mo>(</mo><mrow><mn>2</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa166">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p346"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2557" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mo>+</mo><mn>3</mn><mi>i</mi></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>5</mn><mo>−</mo><mn>2</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa167">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p348"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2559" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>4</mn><mo>+</mo><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa168">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p350"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2561" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>8</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa169">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p352"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2563" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>3</mn><mo>+</mo><mn>2</mn><mi>i</mi></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>3</mn><mo>−</mo><mn>2</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa170">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p354"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2564" display="inline"><mrow><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>1</mn><mo>+</mo><mn>5</mn><mi>i</mi></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mtext>−</mtext><mn>1</mn><mo>−</mo><mn>5</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa171">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2565" display="block"><mrow><mfrac><mrow><mn>2</mn><mo>+</mo><mn>9</mn><mi>i</mi></mrow><mrow><mn>2</mn><mi>i</mi></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa172">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2567" display="block"><mrow><mfrac><mi>i</mi><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>i</mi></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa173">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2569" display="block"><mrow><mfrac><mrow><mn>4</mn><mo>+</mo><mn>5</mn><mi>i</mi></mrow><mrow><mn>2</mn><mo>−</mo><mi>i</mi></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa174">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2571" display="block"><mrow><mfrac><mrow><mn>3</mn><mo>−</mo><mn>2</mn><mi>i</mi></mrow><mrow><mn>3</mn><mo>+</mo><mn>2</mn><mi>i</mi></mrow></mfrac></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa175">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p364"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2573" display="inline"><mrow><mn>10</mn><mo>−</mo><mn>5</mn><msup><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa176">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p366"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2575" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><mo>)</mo></mrow><mo>+</mo><mn>4</mn></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa177">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2577" display="block"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi>i</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa178">
<div class="question">
<span class="informalequation"><math xml:id="fwk-redden-ch05_m2579" display="block"><mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>i</mi></mrow><mrow><mn>3</mn><mi>i</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa179">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p372"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2581" display="inline"><mrow><msqrt><mrow><mtext>−</mtext><mn>8</mn></mrow></msqrt><mrow><mo>(</mo><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mrow><mtext>−</mtext><mn>4</mn></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa180">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p374"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2583" display="inline"><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msqrt><mrow><mtext>−</mtext><mn>18</mn></mrow></msqrt></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>3</mn><mo>−</mo><msqrt><mrow><mtext>−</mtext><mn>2</mn></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></math></span></p>
</div>
</li>
<li class="qandaentry" id="fwk-redden-ch05_s08_qs01_qa181">
<div class="question">
<p class="para" id="fwk-redden-ch05_s08_qs01_p376"><span class="inlineequation"><math xml:id="fwk-redden-ch05_m2585" display="inline"><mrow><msup><mrow><mrow><mo>(</mo><mrow><msqrt><mrow><mtext>−</mtext><mn>5</mn></mrow></msqrt><mo>−</mo><msqrt><mrow><mtext>−</mtext><mn>10</mn></mrow></msqrt></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></math></span></p>
</div>