# publicKhan/khan-exercises

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  2aedc788 » Christi  2012-06-30 estimating square roots 1  cde9e9f4 » jeresig  2013-04-24 Re-run the exercises through the updated cleaner. 2 3  113bddd1 » spicyj  2013-04-11 Update the title tags to match real display names 4 Estimating square roots  ac1415e8 » spicyj  2014-03-05 Use requirejs for module loading 5  2aedc788 » Christi  2012-06-30 estimating square roots 6 7 8
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12 randRange( 2, 11 ) 13 randRange( N * N + 1, (N + 1) * (N + 1) - 1 ) 14
15  0f0c6307 » cbhl  2013-04-16 Clean up the exercise files using the new cleaning utility. (II) 16

The value of \sqrt{Q} lies between which two consecutive integers?

 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
 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
 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
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N < \sqrt{Q} < N + 1

 2aedc788 » Christi  2012-06-30 estimating square roots 24 two integers, like 6 25
 064281ea » beneater  2012-09-19 Fix up exercises that are too wide for tutorials 26  2aedc788 » Christi  2012-06-30 estimating square roots 27
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Consider the perfect squares near Q.  0f0c6307 » cbhl  2013-04-16 Clean up the exercise files using the new cleaning utility. (II) 30 [What are perfect squares?]  2aedc788 » Christi  2012-06-30 estimating square roots 31

 d53a57cf » jeresig  2013-04-16 Two doctypes were being output. Only output one. 32
 2aedc788 » Christi  2012-06-30 estimating square roots 33

34 Perfect squares are integers which can be obtained by squaring an integer. 35

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37 The first 13 perfect squares are: 38

39 \qquad 1,4,9,16,25,36,49,64,81,100,121,144,169 40
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N * N is the nearest perfect square less than Q.

 8fa9a68a » Christi  2012-07-01 oops. Fixed less to more 43

(N + 1) * (N + 1) is the nearest perfect square more than Q.

 95f8b63a » petercollingridge  2014-07-03 Simplify final hints 44

So, N * N < Q < (N + 1) * (N + 1).

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\sqrt{N * N} < \sqrt{Q} < \sqrt{(N + 1)*(N + 1)}

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N < \sqrt{Q} < N + 1

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 2aedc788 » Christi  2012-06-30 estimating square roots 49
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 cde9e9f4 » jeresig  2013-04-24 Re-run the exercises through the updated cleaner. 55 56
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