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Several different derivations of this algorithm are possible. One derivation shows it is a special case of [[Newton's method]] (also called the Newton-Raphson method) for finding zeros of a function <math>f(x)</math> beginning with an initial guess. Although Newton's method is iterative, meaning it approaches the solution through a series of increasingly-accurate guesses, it converges very quickly. The rate of convergence is quadratic, meaning roughly that the number of bits of accuracy doubles on each iteration (so improving a guess from 1 bit to 64 bits of precision requires only 6 iterations). For this reason, this algorithm is often used in computers as a very fast method to calculate square roots.
For large ''n'', the ''n''<sup>th</sup> root algorithm is somewhat less efficient since it requires the computation of <math>x_k^{n-1}</math> at each step, but can be efficiently implemented with a good exponentiation algorithm.
== Derivation from Newton's method ==
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