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 x^{3}.

Therefore,

512 - x^{3} = 387

or - x^{3} = 387 - 512

or - x^{3} = - 125

or x^{3} = 125

or x^{3} = 5^{3}

or x = 5

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

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