Cube of Rational Numbers

Cube of Rational numbers : In the previous sections, we have learnt about the cubes of natural numbers and negative integers. Similarly, we define the cubes of rational numbers which is not an integer as given below.

Rational Number's cube

Let a = m /n be a rational number
(m, n are non zero integers such that n ≠ + or – 1) other than an integer, then the cube of a is defined as
a
3 = a x a x a or
(m/n)
3 = m/n x m/n x m/n = m 3 / n 3

Examples :

1) Find (2/3)
3
Solution:
(2/3)
3 = 2 3 /3 3 = 2 x 2 x 2/ 3 x 3 x 3 = 8 /27
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2) Find
(5 2⁄7) 3
Solution :
5 2⁄7 = 37/7
= 37
3 /7 3
= 37 x 37 x 37/ 7 x 7 x 7
= 50653/343
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3) Find
(3 1⁄10) 3
Solution :
3 1⁄10 = 31/10
= 31
3 /10 3
= 31 x 31 x 31/ 10 x 10 x 10
= 29791/1000
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4) Find (-6/11)
3
Solution:
(-6/11)
3 = (-6) 3 /11 3
= (-6) x (-6) x (-6)/ 11 x 11 x 11
= -216 /1331
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5) Find (-1/10)
3
Solution:
(-1/11)
3 = (-1) 3 /10 3
= (-1) x (-1) x (-1)/ 10 x 10 x 10
= -1 /1000
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6) Find (a/8)
3
Solution:
(a/8)
3 = (a) 3 /8 3
= (a) x (a) x (a)/ 8 x 8 x 8
= a
3 /512

Cube -Cube Roots

Cube-Numbers
Perfect- Cube
Properties : Cube
Cube - Column method
Negative numbers-cube
Cube of Rational numbers
Cube-Root
Finding cube-root by Prime Factorization
Cube- root of Rational numbers
Estimating cube -root

From Cube - rational numbers to Exponents