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

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N

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N < \sqrt{Q} < N + 1

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Consider the perfect squares near Q. 37 [What are perfect squares?] 39

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42 Perfect squares are integers which can be obtained by squaring an integer. 43

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45 The first 13 perfect squares are: 46

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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 51

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

85d66bd minor cleanup Christi authored Jun 30, 2012 52

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)}.

2aedc78 estimating square roots Christi authored Jun 30, 2012 54

So the square root of Q is between N and N + 1.

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