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

CUBEROOT 171 n n c n n c n n c 2 6 6 7 8 0 8 (remainder) 6 5 (line of cube-root) And subtracting the cube of the 'first' (ādima) (i.e. 5³ or 125) from its own place (i.e. from 2667), we get n n c n n c n n c 2 5 4 2 8 0 8 (remainder) 6 5 (line of cube-root) One round of the operation is now over; and the num- ber 65 standing in the line of the cube-root is the cube- root of the given number (277167808) up to its last-but- one 'cube' place ( ghana pada ) from the left (i.e. of 277167), As there is one more 'cube' place (ghana-pada) on the right, the process is repeated. Thus placing the cube- root (i.e. 65) under the third place beginning with the last-but-one 'cube' place (ghana-pada), we have n n c n n c n n c 2 5 4 2 8 0 8 (remainder) 6 5 (line of cube-root) Dividing out 25428 by 3.65² (=12675) as before, and placing the quotient in the line of the cube-root, we have n n c n n c n n c 7 8 0 8 (remainder) 6 5 2 (line of cube-root) Subtracting 3 × 65 × 2² (=780) we get. n n c n n c n n c 8 (remainder) 6 5 2 (line of cube-root) Finally subtracting 2³=8 from 8, we get n n c n n c n n c 0 (remainder) 6 5 2 (line of cube-root) The second round of operation is now over. There being no more of ghana-pada ('cube' place) on the right, the process ends. The quantity in the line of cube root, viz., 652, is the cube-root of the given