ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

CUBEROOT 167 | - | - | 1 8 2 2 5 Subtract square 1 root = 1 Divide by twice ——— the root 2) 8 (3 placing quotient at the 6 next place, the root=13 ——— 22 Subtract square of quotient 9 Divide by twice 26)132(5 placing quotient at the the root 130 next place, the root=135 Subtract square 25 of the quotient 25 The process ends. The square-root of 18225 is thus 135. It has been stated by Kaye, that Āryabhaṭa’s method of finding out the square-root is algebraic in character, and that it resembles the method given by Theon of Alexandria. Ārya- bhaṭa’s method is purely arithmetic and not algebraic is the view of Datta and Singh who do not agree with Kaye on this point. Cube Root The Sanskrit term for cube-root is ghanamūla or ghanapada. The first mention of the operation of cube-root is found in the Āryabhaṭīya of Āryabhaṭa I (499 A.D.), though the operation is given in only a concise form : Divide the second aghana place by thrice the square of the cube-root; subtract from the first aghana place the square of the quotient multiplied by thrice the preceding (cube-root); and (subtract) the cube (of the quotient) from the ghana place; (the quotient put down) at the next place (in the line of the root) gives (the root).¹ As has been explained by all the commentators on the Āryabhaṭīya, the units place is ghana; the tens place is first aghana, the hundreds place is the second aghana, the thousands place is ghana, the ten thousands place is first aghana, the hun-

1. अघनाद् भजेद् द्वितीयात् त्रिगुणेन घनस्य मूलवर्गेण। वर्गस्त्रिपूर्व गुणितश्शोध्यः प्रथमाद् घनश्च घनात् ॥ —Ārya. II. 5