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 non-negative real number. For the square roots of a negative or complex number, see below.

Finding ${\displaystyle {\sqrt {S}}}$ is the same as solving the equation ${\displaystyle f(x)=x^{2}-S=0\,\!}$ for a positive ${\displaystyle x}$. 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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