Mathematics in Ancient and Medieval India c5.s14.1

c5.s14.1

In the *Śulbasūtra*¹, a surd was technically called *karaṇī*. Thus *dvikaraṇī* means √2, *trikaraṇī* = √3, *catuṣkaraṇī* = √4, *saptamakaraṇī* = √7 etc. By *karaṇī*, root of both square and non-square numbers were meant. The idea of terms ‘audible’ for rational number and ‘inaudible’ for irrational number used by the Arabian scholar al-Khwārizmī (c. 825 A.D.) perhaps developed from Hindu term *karaṇī*¹. The Śulba authors knew the operations of addition and multiplication on surd numbers. Only in one instance, Śulba authors viz., Baudhāyana, Āpastamba and Kātyāyana calculated the value of √2 in terms of fraction by following a method of approximation. It has been discussed in the chapter on geometry. This is :