Hero's method

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An iterative method of approximating the square root of a number. If √k is required, and x0 is an initial approximation, then n = 0, 1, 2, … will converge to the square root of k. For example, to calculate the square root of 5, using a first approximation of 2, will give x2=2.236  111  11…, x3=2.236  067  978…, x4=2.236  067  978… and √5 = 2.236067978…. So this method has found the square root to considerable accuracy after only three iterations.

Subjects: Mathematics.

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