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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