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GANITASĀRASANGRAHA.
42. Tell me, O leading arithmetician, the square roots of 110889, 12321, and 844561.
Thus ends aquare root, the fourth of the operations known as Parikarman.
Cubing. The rule of work in relation to the operation of cubing, which is the fifth of the parikarman operations), is as follows:- .
43. The product of (any) three eqnal quantities: or the product obtained by the multiplication of any (given) quantity by that (given quantity) as diminished hy a chosen quantity and (then again) by that (given quantity) as increased by the (samo) chosen quantity, when combined with the square of the chosen quantity as multiplied by the least of the above three qunntities) and combined) also with the cube of the chosen quantity: gives rise to a cubic 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 giveu quantity). Or, the square of the quantity (the cube whoreof is required), when combined with the product (obtained by the multiplication) of this giveu quantity diminished by one by the sum of a serios in arithmetical progrossion in which the first term is one, the common difforence is two and the number of torms is (equal to) the given quantity, (gives rise to the oube of the given quantity).
49. Synbolically expressed, this rule works ont thus: (i) a xaxa=al: (ii) a (a + b)(a-b) + be (a - b)+
b al 44. Algebraically, this rule means
(i) ad == a + 3a + 5a + 7 + .........to a terme. (ii) a=a'+ (a-1) (1+3+5+7+ ........to a terms).