# Khan/khan-exercises

estimating square roots

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Estimating square roots as between two roots + Common Core State Standard: approximately 8.NS + Video coverage: http://www.khanacademy.org/test-prep/cahsee/v/cahsee-practice--problems-1-3 question 2 + Prerequisite: Square roots +
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+ randRange( 2, 11 ) + randRange( N * N + 1, (N + 1) * (N + 1) - 1 ) +
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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

+ two integers, like 6 +
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Consider the perfect squares near Q. + [What are perfect squares?] +

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

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+ The first 13 perfect squares are: +

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

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

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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)}.

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

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