# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२३६

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GAŅIITASĀRASAŃGRAHA.

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:--

18. 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) in relation to fractions.

Examples in illustration thereof.

14. O arithmetician, tell me the squares of ${\displaystyle {\tfrac {5}{2}},{\tfrac {7}{2}},{\tfrac {9}{2}},{\tfrac {16}{3}},{\tfrac {20}{3}},{\tfrac {100}{3}}}$ and ${\displaystyle {\tfrac {200}{3}}}$

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 ${\displaystyle {\tfrac {1}{4}},{\tfrac {1}{9}},{\tfrac {1}{16}},{\tfrac {1}{25}}}$ and ${\displaystyle {\tfrac {1}{36}}}$

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 ${\displaystyle {\tfrac {676}{25}}}$.

18. The following quantities, namely, ${\displaystyle {\tfrac {1}{2}},{\tfrac {1}{3}},{\tfrac {1}{4}},{\tfrac {1}{5}},{\tfrac {1}{6}},{\tfrac {1}{7}},{\tfrac {1}{8}}}$ and ${\displaystyle {\tfrac {1}{9}}}$ 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 ${\displaystyle {\tfrac {676}{25}}}$is given in the original as ${\displaystyle {\tfrac {700-3\times 8}{5^{2}}}}$