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32 CUBE ROOT.
Radical Quantities Expressed without the Radical Sign.
The radical sign is not always used in signifying radical
quantities. Sometimes a quantity expressing a root is written
as a quantity to be raised into a fractional power. For instance :
V 16 may be written I62. This is the same value ; thus,
*/W= 4 and 16^ = 4.
3
V 27 may be written, 27^ = 3.
3 3
8$ = V 82 =V 64 =4.
The denominator in the exponent always indicates which
root is to be extracted. Thus, 8t will be square 8 and extract
the cube root from the product.
Example.
4 4
16l = V163 = V4096 = 8.
Thus, cube 16 and extract the fourth root of the product.
RECIPROCALS.
The reciprocal of any number is the quotient which is ob-
tained when 1 is divided by the number. For instance, the
reciprocal of 4 is % — 0.25 ; the reciprocal of 16 is j
1
^ =
0.0625, etc.
Frequently it is a saving of time when performing long
division to use the reciprocal, as multiplying the dividend by
the reciprocal of the divisor gives the quotient. For instance,
divide 4 by 758. In Table No. 6 the reciprocal of 758 is given
as 0.0013193. Multiplying 0.0013193 by 4 gives 0.0052772,
which is correct to six decimals. When reducing vulgar frac-
tions to decimals the reciprocal may be used with advantage.
For instance, reduce £f to decimals. In Table No. 6 the recip-
rocal of 64 is given as 0.015625, and 15 X 0.015625 == 0.234375,
which is the decimal of £f.
Important.—Whenever the exact reciprocal is not ex-
pressible by decimals the result obtained by its use, as explained
above, is only approximate.
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