पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२३८

40 GANITASĀRASANGRAHA. The Squaring, Square-Root, Cubing, and Cube- Root of Fractions. In connection with the squaring, the square root, the cubing, and the cube root of fractions, the rule 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 newf denominator, there arises the result of the operation of squaiing or of any of the other above-mentioned (operations as the caso may be) in relation to fractions. Examples in illustration thereof 14. O arithmetician, tell me the squares of and 200. 15. The numerators (of the given fractions) begin with 3 and (gradually) 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 quickly, O arithmetician, the square roots of 1, 16, 25 and 6. 17. Here 17. O elever 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 78 18 The following quantities, namely, , , , , , , & 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. 676 25 700-3x 8 5² 16, 20, 100 is given in the original as.