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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.
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