An Algorithm for Computing the n^th Root of Real Numbers using a General Method

Abstract

Based on an old article about extracting the n^th of real numbers using a general method, we introduce an algorithm for computing such roots, using a different approach, through introducing an operator which we define as the inverse binomial operator .We illustrate the procedure by computing n^th roots of some ,randomly, selected real numbers. To show the beauty of using such a new procedure, we compare our calculations with the calculations obtained, for the a certain example, via well-known iteration methods such as the bisection and Newton-Raphson methods; moreover a comparison is made for same purpose using continued fractions method. Finally, a conclusion is given to clarify the advantages of the inverse binomial operator.

Introduction

V. ACKNOWLEDGEMENT

The authors are very thankful to Dr. Yussef A. Awin for his continuous support for the Applied Mathematics Group of the University of Tripoli.

Conclusion

It is shown ,in this work ,that computing the n^th roots of real numbers is still of vital interest and importance .e.g. we point to a method dealing with the determination of the n^th root of positive real numbers, which is a digit-by-digit method up to any desired accuracy [7]. The IBM is also a digit-by-digit method ,and proved to be comparable with NRM and CFM .Extra to that ,the IBM proved to be so precise ,elegant and fruitful. Moreover ,the method can be more beneficial if the algorithm is supported by the right software. Finally, we note that the real number should be positive when we want to extract its n^th root ,when n is even .

References

Awin A.M.(1982) A general method to compute the n^throot of real numbers, International Journal of Mathematical Education in Science and Technology, 13,2, 139-142. Ibran Z.M.,Aljatlawi E.A.,Awin A.M.(2022) On continued fractions and their applications, Journal of Applied Mathematics and Physics,10,142-159. Ibran Z.M.(2014)Continued fractions and their applications, MSc. Thesis, University of Tripoli, Tripoli, Libya, pp 1-87. Awin A.M.(1990) From the new in the world of numbers,1st Edition,Arabiya House for publishing,Tripoli. Awin A.M.( 2010 ) Numerical methods, 1st Edition, University of Misurata publishing,Misurata. Ahmed T.E.,Akrim M.S.,Abdeen K.S.,Awin A.M.(2023) On the computation of zeros of Bessel functions, Journal of Progressive Research in Mathematics,20(1).1-15. Murugesan N.,Ramasamy A.M.S.(2011) A numerical algorithm of the root,Journal of Fundamental Science, 7,1,35-40. http://jfs.ibnusina.utm.my

Copyright

Copyright © 2024 Asmaa A. Altayib, Arij A. Awin, Ali M. Awin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.