# 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 6 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?

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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

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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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