Question

Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, then find the cube root of the larger number.

Answer 1

Given difference of two perfect cubes = 189
and cube root of the smaller number = 3
$\therefore$ Cube of smaller number $=(3{)}^3=27$
Let cube root of the larger number be $x$
Then, cube of larger number $=x^3$
According to the question,
$x^3-27=189\Rightarrow x^3=189+27\Rightarrow x^3=216\Rightarrow x=\sqrt[3]{3216}=\sqrt[3]{36\times 6\times 6}\therefore x=6$
Hence, the cube root of the larger number is 6.