A numerical algorithm for nth root
DOI:
https://doi.org/10.11113/mjfas.v7n1.207Keywords:
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.
References
(a) J. Napier, Mirifici Logarithmorum Canonis Descriptio (1614) and E. Wright (English Translation from Latin), A Description of the Admirable
Table of Logarithms (1616).
(b) J. Napier (1969), A Description of the Admirable Table of Logarithms, London 1616, Amsterdam; New York, N.Y.: Theatrum Orbis Terrarum;
Da Capo Press.
R.G.Dromey, How to solve it by computer, Pearson Education, New Delhi, 2008.
I. Niven and H.Zuckerman, An introduction to the theory of numbers, Wiley Student Edition, New Delhi, 1991.
J. Gower, A note on an iterative method for root extraction, The Computer J., 1(3) (1958), 142-143.
R. Burden and D. Faires, Numerical analysis, Thomson Asia, Bangalore, 2005.
K. Matthews, Computing roots, The College Math. J., 19 (1988), 174- 176.
W. Priestley, From square roots to nth roots, Newton`s method in disguise, The College Math. J., 30:5 (1999), 387-388.
D. Muench and G. Wildenberg, A logarithm algorithm for a five-function calculator, The Two-year College Math. J., 14 (4) (1983), 324-326.
