Question

The difference between two perfect cubes is $189$. If the cube root of the smaller number is $3$, find the cube root of the larger number.

• A. $5$
• B. $6$
• C. $8$
• D. $7$

Answer 1

The correct option is B $6$

Given:
Difference between two perfect cubes $=189$
Cube root of the smaller number $=3$
So, the smaller perfect cube $=3^3=27$
Let’s assume the larger perfect cube to be $a$.
According to the condition given in the question,
$a^3-27=189$
$a^3=189+27=216$
Taking cube root on both sides,
$a={216}^{\frac{1}{3}}=6$
Cube root of the larger number $=6$