# A numerical algorithm for nth root

## Authors

• Natarajan Murugesan
• A.M.S. Ramasamy

## Keywords:

nth root, perfect nth power, non-perfect nth power, blocks, concatenation,

## Abstract

Presently a direct analytical method is available for the digit-by-digit extraction of the square root of a given positive real number. To calculate the nth
root of a given positive real number one may use trial and error method, iterative method, etc. When one desires to determine the nth root, it is found that
such methods are inherent with certain weaknesses like the requirement of an initial guess, a large number of arithmetic operations and several iterative
steps for convergence, etc. There has been no direct method for the determination of the nth root of a given positive real number. This paper focuses
attention on developing a numerical algorithm to determine the digit-by-digit extraction of the nth root of a given positive real number up to any desired
accuracy. Examples are provided to illustrate the algorithm.

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