 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 33 = 27, 53 = 125, etc.
• Cubes of all even numbers are even. Thus 23 = 8, 43 = 64, 63 = 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) $$\sqrt{-a^{3}}=-a$$

(ii) $$\sqrt{a b}=\sqrt a^{a} \sqrt{b}$$

(iii) $$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}, b \neq 0$$

A Pattern of Cube:

13 = 1
22 = 8 = 3 + 5
33 = 27 = 7 + 9 + 11
43 = 64 = 13 + 15 + 17 + 19
53 = 125 = 21 + 23 + 25 + 27 + 29