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How can I approximate the square root of 2 without using a calculator?
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$\sqrt{2}$ lies between 1 and 2 because 12 = 1 and 22 = 4 and 2 is between 1 and 4.

$\sqrt{2}$ lies between 1,4 and 1,5 because 1,42 = 1,96 and 1,52 = 2,25

$\sqrt{2}$ lies between 1,41 and 1,42 because 1,412 = 1,988 1 and 1,422 = 2,016 4 … and so on ….
by Diamond (67,868 points)

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