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

Given different of two perfect cubes = 189

And cube root of the smaller number = 3

∴ Cube of smaller number = (3)³ = 27

Let cube root of the larger number be x.

Then, cube of larger number = x³

According to the question,

x³ – 27 = 189

⇒ x³ = 189 + 27

⇒ x³ = 216

⇒ x = `root(3)(216) = root(3)(6 xx 6 xx 6)`

∴ x = 6

Hence, the cube root of the larger number is 6.