Methods of computing square roots

Graph charting the use of the Babylonian method for approximating the square root of 100 (10) using starting values
x0 = 50,
x0 = 1,
and x0 = −5. Note that using a negative starting value yields the negative root.

In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a nonnegative real number. For the square roots of a negative or complex number, see below.

Finding $\sqrt{S}$ is the same as solving the equation $f(x) = x^2 - S = 0\,\!$ . Therefore, any general numerical root-finding algorithm can be used. Newton's method, for example, reduces in this case to the so-called Babylonian method:

单词	Inverse Square Root
释义	Inverse Square Root 英语百科 Methods of computing square roots In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a nonnegative real number. For the square roots of a negative or complex number, see below. Finding $\sqrt{S}$ is the same as solving the equation $f(x) = x^2 - S = 0\,\!$ . Therefore, any general numerical root-finding algorithm can be used. Newton's method, for example, reduces in this case to the so-called Babylonian method:
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Inverse Square Root

Methods of computing square roots