# Cube of Rational Numbers

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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
a3 = a x a x a or
(m/n)3 = m/n x m/n x m/n = m3/ n3

Examples :

1) Find (2/3)3
Solution:
(2/3)3 = 23/33 = 2 x 2 x 2/ 3 x 3 x 3 = 8 /27
_______________________________________________________________
2) Find (5 2⁄7)3
Solution :
5 2⁄7 = 37/7
= 373/73
= 37 x 37 x 37/ 7 x 7 x 7
= 50653/343
________________________________________________________________
3) Find (3 1⁄10)3
Solution :
3 1⁄10 = 31/10
= 313/103
= 31 x 31 x 31/ 10 x 10 x 10
= 29791/1000
________________________________________________________________
4) Find (-6/11)3
Solution:
(-6/11)3 = (-6)3/113
= (-6) x (-6) x (-6)/ 11 x 11 x 11
= -216 /1331
__________________________________________________________________
5) Find (-1/10)3
Solution:
(-1/11)3 = (-1)3/103
= (-1) x (-1) x (-1)/ 10 x 10 x 10
= -1 /1000
__________________________________________________________________
6) Find (a/8)3
Solution:
(a/8)3 = (a)3/83
= (a) x (a) x (a)/ 8 x 8 x 8
= a3 /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