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Algorithms for calculating square roots

Methods of computing square roots are algorithms for approximating the non-negative square root of a positive real number. Since all square roots of natural numbers, other than of perfect squares, are irrational, square roots can usually only be computed to some finite precision: these methods typically construct a series of increasingly accurate approximations.

Most square root computation methods are iterative: after choosing a suitable initial estimate of , an iterative refinement is performed until some termination criterion is met. One refinement scheme is Heron's method, a special case of Newton's method. If division is much more costly than multiplication, it may be preferable to compute the inverse square root instead.

Other methods are available to compute the square root digit by digit, or using Taylor series. Rational approximations of square roots may be calculated using continued fractio