Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 216

CHAPTER II - ARITHMETICAL OPERATIONS,
19
the number represented by the figure in the next) ghana place (after it is taken into position) the cube (of this same quotient).
54. One (figure in the various groups of three figures) is cubio : two are non-cubic. Divide (the non-cubio figure) by three times the square of the cube root. From the (next) non-cubic (figuro) subtract the syuare of the quotient (obtained as above and) multiplied by three times the previously mentioned (cube-root of the highest cube that can be subtracted from the previous cubic figure) and (then subtract) the cube of the above) quotient (from the next cubic figure as taken into position). With the help of the cube-root-figures (so) obtained (and taken into position, the proccdure is) as before.
Examples in illustration thereof. 55. What is the cube root of the numbers beginning with 1 and ending with 9, all cubed; and of 4913; and of 18608677
56. Extract the cube root of 13824, 36926037 and 618470208.
consist of one or two or three figures, as the case may be. The rule mentioned will be clear from the following worked out example. To extract the cube root of 77308776 :
$. gh. bh. $. yh. th, s, yh. 7 7 3 0 8 1 7 7 6
...
... 42 * 3 48)133(2
96
...
... 22 3 X 4 =
370 48
3228
...
... 42 x 3
5292)322070
31752
4557 ... 6° X 3 X 42 -- 4536
*.
...
216 216
Cube root = 126. The rule does not state what figures constitate the cube root; but it is meant that the cube root is the number made up of the figures which are cubed in this operation, written down in the order from above from left to right