What is the square root of 29?


Quick Answer

To two decimal places, the square roots of 29 are 5.39 and -5.39. Multiplying either of these roots by itself equals 29, therefore satisfying the definition of a square root.

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Full Answer

The easiest way to calculate a square root is to use the square root function on a calculator. However, if one does not have a calculator, then one can use Newton's iteration to approximately calculate the square root. This algorithm gives a first estimate for the square root, x1 = 1/2(1 + 29) = 15. One then needs to put this square root back into the formula as follows to calculate a more accurate second estimate, x2 = 1/2(x1 + 29/x1). Repeat this process, repeating x1 with x2 and so on, to get increasingly accurate estimates.

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