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 237

40
GANITASĀRASANGRAHA.
The Squaring, Square-Root, Cubing, and Cube
Root of Fractions.
In connection with the squaring, the square root, the cubing, and the cabe root of fractions, the role of operation is as follows:
13. If, after getting the square, the square root, the cube (or) the cube root of the (simplified) denominator and numerator (of the given fraction), the (new) numerator (so obtained) is divided by the (similarly new) denominator, there arises the result of the operation of squaring or of any of the other above-mentioned (operations as the case may be) iu relation to fractions.
Examples in illustration thereof. 14. V arithmetician, tell me the squares of 1, 1, , 10, 199 and 200.
15. The numerators of the given fractions) begin with 3 and (gradualls) rise by 2; the denominators begin with 2 and (gradually) rise by 1; the number of these (fractions) is known to be 12. Tell me quickly their squares, you who are foremost among arithmeticians.
16. Tell me quicklý, O arithmetician, the square roots of 1, to the n's and 36
17. O clever man, tell me what the square roots are of the squared quantities which are found in the examples bearing on the) squaring of fractions and also of 67
18. The following quantities, wamely, }, }, }, }, , }, } and }, are given. Tell me their cubes separately.
19. The numerators (of the given fractions) begin with 3, and (gradually rise by 4; the denominators begin with 2 and (gradually rise by 2; the number of such (fractional) terms is 10. Tell me their cubes quickly, O friend who are possessed of keen intelligence in calculation.
17. Here 676 is given in the original as 700** 8.