BRAHMAGUPTA AND ARITHMETIC dred-thousands place is second aghana, and so on. Thus to find out the cube-root, one has to mark out the ghana. first aghana and second aghana places, then the process of finding out the cube-root begins with the subtraction of the greatest cube num- ber from the figures up to the last ghana place. Though this has not been explicitly mentioned in the rule, the commentators say that it is implied in the expression ghanasya mula-vargena etc. (by the square of the cube-root etc.") 168 We are reproducing here an illustration given by Datta and Singh. Example. Find the cube-root of 1953125. The places are divided into groups of three by marking them as below [ghana (1) first aghana (-) and second aghana (-)]: Subtract cube Divide by thrice square of root, i.e. 3.1² Subtract square of quotient mul- tiplied by thrice the previous root, 1.e. 22.3.1 Subtract cube of quotient, i.e. 23 Divide by thrice square of the root. i.e. 3.12² Subtract square of quotient multiplied by thrice the pre- vious root, i. e. 5*3.12 Subtract cube of quotient, i.e. 53 1 9 5 3 1 2 5 1 ...
3)9(2 6 35 12 233 8 432)2251(5 2160 912 900 125 125
(c) Root 1 (a) Placing quotient after the root 1 gives the root 12 (b) (a) Placing quotient after the root 12 gives the root 125 (b) (c) Thus the cube-root=125. From the details given, it would be clear that the present