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2aedc788 » Christi
2012-06-30 estimating square roots
1 <!DOCTYPE html>
cde9e9f4 » jeresig
2013-04-24 Re-run the exercises through the updated cleaner.
2 <html data-require="math subhints">
3 <head>
113bddd1 » spicyj
2013-04-11 Update the title tags to match real display names
4 <title>Estimating square roots</title>
ac1415e8 » spicyj
2014-03-05 Use requirejs for module loading
5 <script data-main="../local-only/main.js" src="../local-only/require.js"></script>
2aedc788 » Christi
2012-06-30 estimating square roots
6 </head>
7 <body>
8 <div class="exercise">
9 <div class="problems">
10 <div id="square">
11 <div class="vars">
12 <var id="N">randRange( 2, 11 )</var>
13 <var id="Q">randRange( N * N + 1, (N + 1) * (N + 1) - 1 )</var>
14 </div>
15
0f0c6307 » cbhl
2013-04-16 Clean up the exercise files using the new cleaning utility. (II)
16 <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>
064281ea » beneater
2012-09-19 Fix up exercises that are too wide for tutorials
17
d53a57cf » jeresig
2013-04-16 Two doctypes were being output. Only output one.
18 <div class="definition" id="consecutive-integers">
3cb073f2 » Christi
2012-07-10 changed to consecutive integers to make eater happy
19 Integers that appear in order when counting, for example 2 and 3.
20 </div>
2aedc788 » Christi
2012-06-30 estimating square roots
21
0f0c6307 » cbhl
2013-04-16 Clean up the exercise files using the new cleaning utility. (II)
22 <div class="solution" data-type="multiple">
23 <p><span class="sol short35" data-forms="integer"><var>N</var></span> <code>&lt; \sqrt{<var>Q</var>} &lt;</code> <span class="sol short35" data-forms="integer"><var>N + 1</var></span></p>
2aedc788 » Christi
2012-06-30 estimating square roots
24 <span class="example">two integers, like <code>6</code></span>
25 </div>
064281ea » beneater
2012-09-19 Fix up exercises that are too wide for tutorials
26
2aedc788 » Christi
2012-06-30 estimating square roots
27 <div class="hints">
28 <div>
29 <p>Consider the perfect squares near <code><var>Q</var></code>.
0f0c6307 » cbhl
2013-04-16 Clean up the exercise files using the new cleaning utility. (II)
30 [<a href="#" class="show-subhint" data-subhint="explain-perfect-square">What are perfect squares?</a>]
2aedc788 » Christi
2012-06-30 estimating square roots
31 </p>
d53a57cf » jeresig
2013-04-16 Two doctypes were being output. Only output one.
32 <div class="subhint" id="explain-perfect-square">
2aedc788 » Christi
2012-06-30 estimating square roots
33 <p>
34 Perfect squares are integers which can be obtained by squaring an integer.
35 </p>
36 <p>
37 The first 13 perfect squares are:
38 </p>
39 <code>\qquad 1,4,9,16,25,36,49,64,81,100,121,144,169</code>
40 </div>
41 </div>
42 <p><code><var>N * N</var></code> is the nearest perfect square less than <code><var>Q</var></code>.</p>
8fa9a68a » Christi
2012-07-01 oops. Fixed less to more
43 <p><code><var>(N + 1) * (N + 1)</var></code> is the nearest perfect square more than <code><var>Q</var></code>.</p>
95f8b63a » petercollingridge
2014-07-03 Simplify final hints
44 <p>So, <code><var>N * N</var> &lt; <var>Q</var> &lt; <var>(N + 1) * (N + 1)</var></code>.</p>
45 <div>
46 <p><code>\sqrt{<var>N * N</var>} &lt; \sqrt{<var>Q</var>} &lt; \sqrt{<var>(N + 1)*(N + 1)</var>}</code></p>
47 <p><code><var>N</var> &lt; \sqrt{<var>Q</var>} &lt; <var>N + 1</var></code></p>
48 </div>
2aedc788 » Christi
2012-06-30 estimating square roots
49 </div>
50
51 </div>
52 </div>
53
54 </div>
cde9e9f4 » jeresig
2013-04-24 Re-run the exercises through the updated cleaner.
55 </body>
56 </html>
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