An Analysis on Extracting Square and Cube Roots by Aryabhata’s Methods

Abstract

Abstract— Finding accurate root of a number is still considered as challenging in computer science community. The only popularly known method to compute root is the long division method of finding square root. Aryabhata contributed two methods similar to long division method to compute square root and cube root. In recent years, his methods have also been studied, explained and tried to implement as computer algorithms.  The explained methods and proposed algorithms fail to give correct results. Some analyses have been made on these methods in order to ascertain why the algorithms fail. Improved algorithms have been provided to give correct result while computing square root or cube root using Aryabhata’s methods.    .

Keywords—cube root, square root, Bino’s Model of multiplication, Large number manipulation, Long division method, Aryabhata’s methods.

 (Article history: Received 12 November 2016 and accepted 30 December 2016)