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estimating square roots

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1 parent 6697bd8 commit 2aedc7882b1c0aecdee5ef87ae9a27d44afe6b58 @Christi Christi committed Jun 30, 2012
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+<!DOCTYPE html>
+<html data-require="math math-format word-problems subhints">
+<head>
+ <title>Square roots 2</title>
+ <script src="../khan-exercise.js"></script>
+ <style type="text/css">
+ #answer_area input[type=text] {
+ width: 30px;
+ }
+ </style>
+</head>
+<body>
+ <div class="summary">Estimating square roots as between two roots
+ Common Core State Standard: approximately 8.NS
+ Video coverage: http://www.khanacademy.org/test-prep/cahsee/v/cahsee-practice--problems-1-3 question 2
+ Prerequisite: Square roots
+ </div>
+ <div class="exercise">
+ <div class="problems">
+ <div id="square">
+ <div class="vars">
+ <var id="N">randRange( 2, 11 )</var>
+ <var id="Q">randRange( N * N + 1, (N + 1) * (N + 1) - 1 )</var>
+ </div>
+
+ <p class="question">The value of <code>\sqrt{<var>Q</var>}</code> lies between which two integers?</p>
+
+ <p class="solution"><var>N</var></p>
+ <div class="solution" data-type="multiple">
+ <p><span class="sol short"><var>N</var></span> <code>&lt; \sqrt{<var>Q</var>} &lt;</code> <span class="sol short"><var>N + 1</var></span></p>
+ <span class="example">two integers, like <code>6</code></span>
+ </div>
+
+ <div class="hints">
+ <div>
+ <p>Consider the perfect squares near <code><var>Q</var></code>.
+ [<a href="#" class="show-subhint"
+ data-subhint="explain-perfect-square">What are perfect squares?</a>]
+ </p>
+ <div class="subhint" id="explain-perfect-square">
+ <p>
+ Perfect squares are integers which can be obtained by squaring an integer.
+ </p>
+ <p>
+ The first 13 perfect squares are:
+ </p>
+ <code>\qquad 1,4,9,16,25,36,49,64,81,100,121,144,169</code>
+ </div>
+ </div>
+ <p><code><var>N * N</var></code> is the nearest perfect square less than <code><var>Q</var></code>.</p>
+ <p><code><var>(N + 1) * (N + 1)</var></code> is the nearest perfect square less than <code><var>Q</var></code>.</p>
+ <p>So, we know <code><var>N * N</var> &lt; <var>Q</var> &lt; <var>(N+1)*(N+1)</var></code>.</p>
+ <p>So, <code>\sqrt{<var>N * N</var>} &lt; \sqrt{<var>Q</var>} &lt; \sqrt{<var>(N+1)*(N+1)</var>}</code>.</p>
+ <p class="final_answer">So the square root of <code><var>Q</var></code> is between <code><var>N</var></code> and <code><var>N + 1</var></code>.</p>
+ </div>
+
+ </div>
+ </div>
+
+ </div>
+</body>
+</html>

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