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New exercise: Multiplying radicals

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+<!DOCTYPE html>
+<html data-require="math math-format expressions">
+<head>
+ <meta charset="UTF-8" />
+ <title>Multiplying radicals</title>
+ <script src="../khan-exercise.js"></script>
+</head>
+<body>
+ <div class="exercise">
+ <div class="vars">
+ <var id="PRIMES">shuffle([2, 3, 5, 7, 11, 13])</var>
+ </div>
+ <div class="problems">
+ <div id="simplify" data-weight="3">
+ <div class="vars">
+ <var id="START_INT">randRange( 2, 12 )</var>
+ <var id="RADICAL_INT">randRange( 2, 5 )</var>
+ <var id="RADICAL_PRIME">PRIMES[0]</var>
+ <var id="RADICAL_TOTAL">pow( RADICAL_INT, 2 ) * RADICAL_PRIME</var>
+ </div>
+ <p class="question">Simplify the following expression:</p>
+ <p><code><var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code>.</p>
+ <div class="solution" data-type="radical"><var>pow( START_INT, 2 ) * RADICAL_TOTAL</var></div>
+ <div class="hints">
+ <p>First, try to factor a perfect square out of the radical.</p>
+ <div>
+ <p><code>= <var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code></p>
+ <p><code>= <var>START_INT</var>\sqrt{<var>pow( RADICAL_INT , 2 )</var> \cdot </span><var>RADICAL_PRIME</var>}</code></p>
+ </div>
+ <p>Separate the radical and simplify.</p>
+ <div>
+ <p><code>= <var>START_INT</var>\sqrt{<var>pow( RADICAL_INT , 2 )</var>} \cdot \sqrt{<var>RADICAL_PRIME</var>}</code></p>
+ <p><code>= <var>START_INT</var> \cdot <var>RADICAL_INT</var> \cdot \sqrt{<var>RADICAL_PRIME</var>}</code></p>
+ </div>
+ <p><code>= <var>START_INT * RADICAL_INT</var>\sqrt{<var>RADICAL_PRIME</var>}</code></p>
+ </div>
+ </div>
+ <div id="already-simplified" data-weight="1">
+ <div class="vars">
+ <var id="START_INT">randRange( 2, 12 )</var>
+ <var id="RADICAL_TOTAL">PRIMES[0] * PRIMES[1]</var>
+ </div>
+ <p class="question">Simplify the following expression:</p>
+ <p><code><var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code>.</p>
+ <div class="solution" data-type="radical"><var>pow( START_INT, 2 ) * RADICAL_TOTAL</var></div>
+ <div class="hints">
+ <p>There are no perfect-square factors of <var>RADICAL_TOTAL</var>.</p>
+ <div>
+ <p>Thus, the expression is already in its most simplified form.</p>
+ <p><code>= <var>START_INT</var>\sqrt{<var>RADICAL_TOTAL</var>}</code></p>
+ </div>
+ </div>
+ </div>
+ </div>
+ </div>
+ </div>
+</body>
+</html>
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