Question

Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number.

Answer 1

From the question it is given that,

Difference of two perfect cubes = 189

The cube root of the smaller of the two numbers = 3

So, cube of smaller number = 3³

= 3 × 3 × 3

= 27

Let us assume the cube root of larger number be a³

Then,

As per the condition given in the question,

a³ – 27 = 189

a³ = 189 + 27

a³ =216

By taking cube root on both side,

a = ³√216

a = ³√(6 × 6 × 6)

a = ³√(6³)

a = 6

∴The cube root of the larger number is 6.