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3fbf84f @smenks13 New exercise: Multiplying radicals
smenks13 authored
1 <!DOCTYPE html>
2 <html data-require="math math-format expressions">
3 <head>
4 <meta charset="UTF-8" />
5 <title>Multiplying radicals</title>
6 <script src="../khan-exercise.js"></script>
7 </head>
8 <body>
9 <div class="exercise">
10 <div class="vars">
11 <var id="PRIMES">shuffle([2, 3, 5, 7, 11, 13])</var>
12 </div>
13 <div class="problems">
14 <div id="simplify" data-weight="3">
15 <div class="vars">
16 <var id="START_INT">randRange( 2, 12 )</var>
17 <var id="RADICAL_INT">randRange( 2, 5 )</var>
18 <var id="RADICAL_PRIME">PRIMES[0]</var>
19 <var id="RADICAL_TOTAL">pow( RADICAL_INT, 2 ) * RADICAL_PRIME</var>
20 </div>
21 <p class="question">Simplify the following expression:</p>
22 <p><code><var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code>.</p>
23 <div class="solution" data-type="radical"><var>pow( START_INT, 2 ) * RADICAL_TOTAL</var></div>
24 <div class="hints">
25 <p>First, try to factor a perfect square out of the radical.</p>
26 <div>
27 <p><code>= <var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code></p>
28 <p><code>= <var>START_INT</var>\sqrt{<var>pow( RADICAL_INT , 2 )</var> \cdot </span><var>RADICAL_PRIME</var>}</code></p>
29 </div>
30 <p>Separate the radical and simplify.</p>
31 <div>
32 <p><code>= <var>START_INT</var>\sqrt{<var>pow( RADICAL_INT , 2 )</var>} \cdot \sqrt{<var>RADICAL_PRIME</var>}</code></p>
33 <p><code>= <var>START_INT</var> \cdot <var>RADICAL_INT</var> \cdot \sqrt{<var>RADICAL_PRIME</var>}</code></p>
34 </div>
35 <p><code>= <var>START_INT * RADICAL_INT</var>\sqrt{<var>RADICAL_PRIME</var>}</code></p>
36 </div>
37 </div>
38 <div id="already-simplified" data-weight="1">
39 <div class="vars">
40 <var id="START_INT">randRange( 2, 12 )</var>
41 <var id="RADICAL_TOTAL">PRIMES[0] * PRIMES[1]</var>
42 </div>
43 <p class="question">Simplify the following expression:</p>
44 <p><code><var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code>.</p>
45 <div class="solution" data-type="radical"><var>pow( START_INT, 2 ) * RADICAL_TOTAL</var></div>
46 <div class="hints">
47 <p>There are no perfect-square factors of <var>RADICAL_TOTAL</var>.</p>
48 <div>
49 <p>Thus, the expression is already in its most simplified form.</p>
50 <p><code>= <var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code></p>
51 </div>
52 </div>
53 </div>
54 </div>
55 </div>
56 </div>
57 </body>
58 </html>
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