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.

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.

Question: The difference of the 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.

Answer: 

Given: 

The difference of the two perfect cubes is 387. 

The cube root of the greater of two numbers is 8.

To find: 

We have to find the cube root of the smaller number.

Assumption:

Let the cube root of the smaller number be x.

So, we need to find the value of x.

Solution: 

The difference of the two perfect cubes is 387. 

The cube root of the greater of two numbers is 8. 

This implies, The greater of the two numbers = Cube of 8 = (8)3= 8 x 8 x 8 = 512. 

Let the smaller number be x3

Therefore, 

512 - x3 = 387

or - x3 = 387 - 512

or - x3 = - 125

or x3 = 125

or x3 = 53

or x = 5

Hence, This implies, The cube root of the smaller number is 5.

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