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CUBE ROOT. 31
Example 1.
Extract the cube root of 275,894,451.
Solution
:
\/275 894
= 216
300 X 62 = 10800 ) 59894
451
10800 X 5 + 30 X 6 X 52
+, 53 = 58625
300 X 652 = 1267500 ) 1269451
1267500 X 1 + 30 X 65 X l 2
+ l 3 = 1269451
= 651
0000000
Thus
:
3 _
«/275,894,451 = 651, because 651 X 651 X 651 = 275,894,451.
Example 2 :
Extract the cube root of 551.368.
Solution
:
3
\/551j
5
= 512
300 X 82 = 19200 ) 39368
19200 X 2 + 30 X 8 X 22
+ 23 = 39368
= 8.2
00000
The square root of a number consisting of two figures
will never consist of more than one figure, and the square
root of a number consisting of four figures will never consist of
more than two figures ; hence, the rule to divide numbers into
periods consisting of two figures.
The cube root of a number consisting of three figures will
never consist of more than one figure, and the cube root of a
number consisting of six figures will never consist of more than
two figures ; hence, the rule to divide the numbers into periods
consisting of three figures.
There will always be one decimal in the root for each
period of decimals in the number of which the root is extracted.
This relates to both cube and square root.
The root of a fraction may be found by extracting the
separate roots of numerator and denominator, or the fraction
may be first reduced to a decimal fraction before the root is
extracted.
The root of a mixed number may be extracted by first re-
ducing the number to an improper fraction and then extracting
the separate roots of numerator and denominator, or the number
may be first reduced to consist of integer and decimal fractions,
and the root extracted as usual.
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