# Khan/khan-exercises

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 2aedc78 estimating square roots Christi authored Jun 30, 2012 1 85d66bd minor cleanup Christi authored Jun 30, 2012 2 2aedc78 estimating square roots Christi authored Jun 30, 2012 3 4 Square roots 2 5 064281e Fix up exercises that are too wide for tutorials beneater authored Sep 19, 2012 6 2aedc78 estimating square roots Christi authored Jun 30, 2012 11 12 13
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
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22 randRange( 2, 11 ) 23 randRange( N * N + 1, (N + 1) * (N + 1) - 1 ) 24
25 3cb073f changed to consecutive integers to make eater happy Christi authored Jul 10, 2012 26

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

064281e Fix up exercises that are too wide for tutorials beneater authored Sep 19, 2012 27 3cb073f changed to consecutive integers to make eater happy Christi authored Jul 11, 2012 28
29 Integers that appear in order when counting, for example 2 and 3. 30
2aedc78 estimating square roots Christi authored Jun 30, 2012 31 32

N

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N < \sqrt{Q} < N + 1

35 two integers, like 6 36
064281e Fix up exercises that are too wide for tutorials beneater authored Sep 19, 2012 37 2aedc78 estimating square roots Christi authored Jun 30, 2012 38
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Consider the perfect squares near Q. 41 [What are perfect squares?] 43

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46 Perfect squares are integers which can be obtained by squaring an integer. 47

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49 The first 13 perfect squares are: 50

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N * N is the nearest perfect square less than Q.

8fa9a68 oops. Fixed less to more Christi authored Jul 1, 2012 55

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

85d66bd minor cleanup Christi authored Jun 30, 2012 56

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

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

6ae91a2 . Change square_roots to use sqrt symbol. . Use final_solution class … khirasaki authored Jul 18, 2012 58

So \sqrt{Q} is between N and N + 1.

2aedc78 estimating square roots Christi authored Jun 30, 2012 59
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