This work discusses several methods for estimating the square root of a number, with particular focus on high-speed techniques for approximating the square root of a single value as well as the square root of a sum of squares for quadrature (I/Q) vector magnitude estimation. The paper presents the Newton-Raphson inverse method and the nonlinear IIR filter method for estimating the square root of a single value using iterative methods. It also presents the binary-shift magnitude estimation method and the equiripple-error magnitude estimation method for estimating the magnitude of a complex number.
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Allie et al. (2005) studied this question.
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