Extending the Aryabhatan algorithm for the extraction of higher order roots

In schools, children are taught algorithm for extracting the square and cube roots of a number. However, they are not informed that Aryabhata (b. 476 CE) was the first Indian mathematician to present a systematic algorithm for the extraction of the square and cube root of a number. This algorithm has been succinctly presented by Aryabhata in two successive verses in the Ganitapada of his Aryabhatiyam composed in 499 CE. A careful study of the algorithm given by Aryabhata shows that it can be easily extended to find higher order roots. It also clearly reveals that the decimal place value system should have been in vogue in India for quite a long time before him, because this algorithm is heavily based on a thorough understanding of the decimal place value system. In our paper, we will discuss some of these aspects as well as outline how his algorithm can be extended to find the higher order roots.