पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२१६

18 GANITASARASANGRAHA. 50. The number 213 is cubed; and twice, thrice, four times and five times that (number are) also (cubed; find out the corre- sponding quantities). 51. It is seen that 168 multiplied by all the numbers from 1 to 8 is related (as base) to the required cubes. Give out those enbes quickly. 52. O you, who have seen the other shore of the deep and excellent ocean of the practice of (arithmetical) operations, write down the figures 4, 0, 6, 0,5, aud 9 in order (from right to left), and work out the cube of the number (represented by those figures), and mention the result at once. Thus ends cubing, the fifth of the operations known as Parıkarman. Cube Root. The rule of work in relation to the operation of extract- ing the cube root, which is the sixth (among the parkarman operations), is as follows:-- 53. From (the number represented by the figures up to) the last ghana place, subtract the (highest possible) cube; then divide the (number represented by the next) bhajya place (after it is taken into position) by three times the square of the root (of that cube): then subtract from the (number represented by the next) odhya place (after it is taken into position) tho square of the (above) quotient as multiplied by three and by the already men- tioned (root of the highest possible cube); and then (subtract) from 53 and 51. The figures in any given number, the cube-root whereof is required, are conceived in these rules to be divided into groaps, each of which consists as far as possible of three figures, named, in the order from right to left, as ghana or that which is cubic, that is, from which the cube is to be subtracted, as śödhya or that which is to be subtracted from, and as bhajya or that which is to be divided. The bhajya and sodhya are also known as aghana or non-cubic. The last group on the left need not always consist of all these three figures; it may