Taylor Series
If N is an approximation to, a better approximation can be found by using the Taylor series of the square root function:
As an iterative method, the order of convergence is equal to the number of terms used. With 2 terms, it is identical to the Babylonian method; With 3 terms, each iteration takes almost as many operations as the Bakhshali approximation, but converges more slowly. Therefore, this is not a particularly efficient way of calculation. To maximize the rate of convergence, choose N so that is as small as possible.
Read more about this topic: Methods Of Computing Square Roots
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