16 GANITASARASANGRAHA 1 42. Tell me, O leading arithmetician, the square roots of 120889, 12321, and 844561. Thus ends square root, the fourth of the operations known as Perikarman Cubing. The rule of work in relation to the operation of cubing, which is the fifth (of the parilarman operations), is as follows:- 43. The product of (any) three equal quantities: or the pro- duct obtained by the multiplication of any (given) quantity by that (given quantity) as diminished by a chosen quantity and (then again) by that (given quantity) as increased by the (same) chosen quantity, when combined with the square of the chosen quantity as multiplied by the least (of the above three quantities) and (combined) also with the cube of the chosen quantity: gives rise to a cubie quantity. 44 Or, the summing up of a series in arithmetical progression, of which the first term is the quantity (the cube whereof is) required, the common difference is twice this quantity, and the number of terms is (equal to) this (same given) quantity, (gives rise to the cube of the given quantity). Or, the square of the quantity (the cube whereof is required), when combined with the product (obtained by the multiplication) of this given quantity diminished by one by the sum of a series in arithmetical progres- sion in which the first term is one, the common difference is two and the number of terms is (equal to) the given quantity, (gives rise to the cube of the given quantity). 43. Symbolically expressed, this rule works out thus (i) axaxa=a³ (ii) a (a+b) (a-b) + b² (a−b) + b³ = a³. 44. Algebraically, this rule means- (i) a³a+3a+5a+7a+. .... ..to a terms. (i) a³a²+ (a-1) (1+3+5+7+.........to a terms).
