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2aedc78 @Christi estimating square roots
Christi authored
1 <!DOCTYPE html>
85d66bd @Christi minor cleanup
Christi authored
2 <html data-require="math subhints">
2aedc78 @Christi estimating square roots
Christi authored
3 <head>
4 <title>Square roots 2</title>
5 <script src="../khan-exercise.js"></script>
064281e @beneater Fix up exercises that are too wide for tutorials
beneater authored
6 <style type="text/css">
7 #answer_area input[type=text] {
8 width: 35px;
9 }
10 </style>
2aedc78 @Christi estimating square roots
Christi authored
11 </head>
12 <body>
13 <div class="summary">Estimating square roots as between two roots
14 Common Core State Standard: approximately 8.NS
15 Video coverage: http://www.khanacademy.org/test-prep/cahsee/v/cahsee-practice--problems-1-3 question 2
16 Prerequisite: Square roots
17 </div>
18 <div class="exercise">
19 <div class="problems">
20 <div id="square">
21 <div class="vars">
22 <var id="N">randRange( 2, 11 )</var>
23 <var id="Q">randRange( N * N + 1, (N + 1) * (N + 1) - 1 )</var>
24 </div>
25
3cb073f @Christi changed to consecutive integers to make eater happy
Christi authored
26 <p class="question">The value of <code>\sqrt{<var>Q</var>}</code> lies between which two <a href="#" class="show-definition" data-definition="consecutive-integers">consecutive integers</a>?</p>
064281e @beneater Fix up exercises that are too wide for tutorials
beneater authored
27
3cb073f @Christi changed to consecutive integers to make eater happy
Christi authored
28 <div class="definition" id="consecutive-integers">
29 Integers that appear in order when counting, for example 2 and 3.
30 </div>
2aedc78 @Christi estimating square roots
Christi authored
31
32 <p class="solution"><var>N</var></p>
33 <div class="solution" data-type="multiple">
34 <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>
35 <span class="example">two integers, like <code>6</code></span>
36 </div>
064281e @beneater Fix up exercises that are too wide for tutorials
beneater authored
37
2aedc78 @Christi estimating square roots
Christi authored
38 <div class="hints">
39 <div>
40 <p>Consider the perfect squares near <code><var>Q</var></code>.
41 [<a href="#" class="show-subhint"
42 data-subhint="explain-perfect-square">What are perfect squares?</a>]
43 </p>
44 <div class="subhint" id="explain-perfect-square">
45 <p>
46 Perfect squares are integers which can be obtained by squaring an integer.
47 </p>
48 <p>
49 The first 13 perfect squares are:
50 </p>
51 <code>\qquad 1,4,9,16,25,36,49,64,81,100,121,144,169</code>
52 </div>
53 </div>
54 <p><code><var>N * N</var></code> is the nearest perfect square less than <code><var>Q</var></code>.</p>
8fa9a68 @Christi oops. Fixed less to more
Christi authored
55 <p><code><var>(N + 1) * (N + 1)</var></code> is the nearest perfect square more than <code><var>Q</var></code>.</p>
85d66bd @Christi minor cleanup
Christi authored
56 <p>So, we know <code><var>N * N</var> &lt; <var>Q</var> &lt; <var>(N + 1) * (N + 1)</var></code>.</p>
57 <p>So, <code>\sqrt{<var>N * N</var>} &lt; \sqrt{<var>Q</var>} &lt; \sqrt{<var>(N + 1)*(N + 1)</var>}</code>.</p>
6ae91a2 @khirasaki . Change square_roots to use sqrt symbol. . Use final_solution class whe...
khirasaki authored
58 <p class="final_answer">So <code>\sqrt{<var>Q</var>}</code> is between <code><var>N</var></code> and <code><var>N + 1</var></code>.</p>
2aedc78 @Christi estimating square roots
Christi authored
59 </div>
60
61 </div>
62 </div>
63
64 </div>
65 </body>
66 </html>
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