पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२१५

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एतत् पृष्ठम् परिष्कृतम् अस्ति
19
CHAPTER II - ARITHMETICAL OPERATIONS.

the (number represented by the figure in the next) ghana place (after it is takon into position) the cube (of this same quotient).

54. One (figure in the various groups of three figures) is cubic: two are non-cubic. Divide (the non-cubic figure) by three times the square of the cube root. From the (next) non-cubic (figure) subtract the square 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) tho cube of the (above, quotient (from the next cubic figure as taken into position). With the help of the cuberoot-figures (s0) obtained (and taken into position, the procedure is) as beforo.


Examples in thstation thereof:

55. What is the cube root of the numbers beginning with 1 and ending with 9, all cubed; and of 4913; and of 1860867?

56. Extract the cube root of 13824, 36926037 and 618470908.


consist of one or two or three figures, as the cause may be . The rule mentioned will be clear from the following worked out example.


To extract the cube root of 17808776:--
ś   gh.   bh.   ś   gh.   bh.   ś   gh.
7    7   |   3    0   8   |   7    7    6
gh.     ...          ...     43          ==          6 4 
bh.     ...          ...  42 x 3      ==       48)133(2
     96 
    370
s.     ...          ...  22  x  3   x  4   ==       48 
 3228
gh.   ...          ...  23          ==          8
bh.   ...          ...  422  x  3 ==    5292)32207(6
      31752
  4557
ś.     ...          ...  62  x  3   x  42   ==   4536
   216
gh.   ...          ...  63          ==             216
Cube root == 426

The rule does not state what figures constitute 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