In this chapter, we present an ancient Indian algorithm for extracting roots. The algorithm is a reconstruction based on a formula found in the Śulbasūtras, early Sanskrit texts associated with the Vedic tradition. We show that this procedure can be generalized to compute roots of arbitrary integers and rational numbers. Its rate of convergence is analyzed, and connections are established with more widely known methods of root extraction, such as the Heron and Newton methods. The algorithm also provides a natural way to demonstrate that the roots of non-square integers are irrational. In this way, it reveals an unexpected depth and potential for further mathematical insight.