Question

If a and b are coprime, what should $a^3$ $b^2$ be multiplied with to make it a perfect cube?

• A. True
• B. False
• C. $b$
• D. $a^2$ $b$

Answer 1

The correct option is C $b$

$a^3$ $b^2$ = a $\times$ a $\times$ a $\times$ b $\times$ b
A perfect cube is a result of multiplying a number three times by itself, or, in other words, it is an integer to the power 3.
$a^3$ $b^2$ can be a perfect cube if 'b' is a perfect cube in the first place. But since it is given 'a' and 'b' are prime numbers, b can not be a perfect cube.
As b has only two as power on itself, if we multiply $a^3$ $b^2$ with one more 'b' it becomes a perfect cube.