NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.1

Ex.1  Find the value of the following: 7³ – 6³

Soln: 7³ – 6³

7³ – 6³ = (7- 6)(7² + (7*6) + 6²) ……….. Using the formula ( a³ - b³ )= ( a - b ) (a² + ab + b²)

=(1)(49+42+36)

= 127

Ex.2 If the difference between two perfect cubes is 189, and if the cube root of the smaller of the two numbers is 3, determine the cube root of the larger number.

Soln: Given the difference of two perfect cubes =189.

Let the smaller cube number = x.

Then the other cube (larger cube) = 189 + x

Given cube root of the smaller cube = 3

Therefore,

∛x = 3

Therefore, x = 3³

 = 27.

Larger cube = 189 + 27 = 216

Cube root of the larger cube number = ∛216

 = 6.