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