Question

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.

Answer 1

Given,
The difference in two cubes $=387$
And, the cube root of the greatest number $=8$
So, the greatest number $=(8{)}^3=8\times 8\times 8=512$
Hence, the second number $=512-387=125$
Thus,
The cube root of $125$ is
$=\sqrt[3]{3125}=\sqrt[3]{35\times 5\times 5}=5$