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<!DOCTYPE html>
<html data-require="math math-format expressions">
<head>
<meta http-equiv="Content-Type" content="text/html; 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 <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>
</body>
</html>
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