What are some tricks for calculating square roots?


Quick Answer

To estimate a square root without a calculator, determine the two perfect squares that come before and after the given number. Then using the square roots of the perfect squares as guides, estimate the given number���s square root based on its placement between the two perfect squares.

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What are some tricks for calculating square roots?
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Full Answer

For example, 34 is between the perfect squares of 25 (5 x 5) and 36 (6 x 6). Therefore, 34 is approximately 5.8, as 34 is closer to 36 than to 25. For a more accurate estimation, divide the given number (34) by the approximation (5.8). Average this answer (approximately 5.862) with the approximation (5.8) to yield a closer estimation of the square root of the given number (approximately 5.831). Continue this process until the desired accuracy of the estimate is reached.

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