Question

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

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

The correct option is B 6

From the question it is given that,
Difference of two perfect cubes = 189
The cube root of the smaller of the two numbers = 3
So, cube of smaller number $=3^3=27$
Let us assume the cube root of larger number be $a$
Then, as per condition given in the question,
$a^3-27=189a^3=189+27=216$
By taking cube root on both sides,
$a={216}^{\frac{1}{3}}=6$
The cube root of larger number = 6