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30 cube root.
Example 2.
Extract the square root of 26.6256.
Solution
:
V26|62:56
52 = 25
J
20 X 5 = 100 ) 162
100 X 1 + l 2 = 101
1
20 X 51 = 1020 ) 6156
1020 X 6 + 62 = 6156
= 5.16
0000
CUBE ROOT.
Wher the cube root is to be extracted, the number is
divided into periods consisting of three figures. Commencing
from the extreme right if the number has no decimals, or from
the decimal point, toward the left, for the whole number, and
toward the right for the decimals. (If the last period of deci-
mals should not have three figures, then annex ciphers until
this period also has three figures, but if the period to the
extreme left in the integer should happen to consist of less than
three figures it makes no difference ; leave it as it is.) Ascer-
tain highest cube root in the first period and place it to the
right of the number, the same as in long division. Cube this
root and subtract the product from the first period. To the
remainder annex next period of numbers. For the divisor in
this number take 300 times the square of the part of the root
already found,* and the quotient is the next figure in the root, if
the product of this figure multiplied by the divisor and added
to 30 times the part of the root already found, multiplied by the
square of this quotient and added to the cube of the quotient,
does not exceed this dividend. To the difference between this
sum and the dividend is annexed the next period of numbers.
For divisor take again 300 times the square of the part of the
root already found, etc. Continue in this manner until the last
period is used. If there is any remainder from last period, and
a more exact root is required, ciphers may be annexed three at
a time, and the operation continued until as many decimals are
obtained in the root as are wanted.
* If this divisor exceeds the dividend, write a cipher in the root, annex the next
period of numbers, calculating a new divisor corresponding to the increased root,
and proceed as explained.
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