On this page, you will find Cubes and Cube Roots Class 8 Notes Maths Chapter 7 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 7 Cubes and Cube Roots will seemingly help them to revise the important concepts in less time.

## CBSE Class 8 Maths Chapter 7 Notes Cubes and Cube Roots

### Cubes and Cube Roots Class 8 Notes Conceptual Facts

- A natural number n is a perfect cube if there exists a natural number m such that m x m x m = n For example: 1, 8, 27 …. are all perfect cubes

Properties of Cubes of Numbers:

- Cubes of all odd numbers are odd. Thus 3
^{3}= 27, 5^{3}= 125, etc. - Cubes of all even numbers are even. Thus 2
^{3}= 8, 4^{3}= 64, 6^{3}= 216, etc. - Cubes of all negative numbers are always negative. Thus (-1)
^{3}= -1, (-2)^{3}= -8, (-3)^{3}= -27, etc. - \(\left(\frac{a}{b}\right)^{3}=\frac{a^{3}}{b^{3}}\)

Properties of Cube Roots:

(i) \(\sqrt[3]{-a^{3}}=-a\)

(ii) \(\sqrt[3]{a b}=\sqrt[3] a^{a} \sqrt[3]{b}\)

(iii) \(\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}, b \neq 0\)

A Pattern of Cube:

1^{3} = 1

2^{2} = 8 = 3 + 5

3^{3} = 27 = 7 + 9 + 11

4^{3} = 64 = 13 + 15 + 17 + 19

5^{3} = 125 = 21 + 23 + 25 + 27 + 29