Difference of two perfect cubes is 387. If the cube root of the greater of two numbers is 8, find the cube root of the smaller number.

Given :

Difference of two perfect cubes is 387.  Cube root of the greater of two numbers is 8.

To find :

We have to find the cube root of the smaller number, that is, x

Solution :

Difference of two perfect cubes is 387.  Cube root of the greater of two numbers is 8.

This implies,

The greater of the two numbers = Cube of 8 = 8³= 512.

Let the smaller number be x³.

Therefore,

512$-x^3=387$

$x^3=512-387$

$x^3=125$

$x^3=5\times5\times5$

$x^3=5^3$

This implies,

$x=5$

The cube root of the smaller number is 5.