Question

What should be multiplied with $x^2{y}^3$ to make it a perfect cube, if $x$ and $y$ are prime numbers?

• A. $x$
• B. $x^2$
• C. $x^3$
• D. $xy$

Answer 1

The correct option is A $x$

$x^2{y}^3=x\times x\times y\times y\times y$
A perfect cube is a result of multiplying a number three times by itself, or, in other words, it is an integer to the exponent 3.

$x^2{y}^3$ can be a perfect cube if '$x$' is a perfect cube in the first place. But since it is given '$x$' and '$y$' are prime numbers, '$x$' can not be a perfect cube.

As '$x$' has two as exponent on itself, if we multiply $x^2{y}^3$ with one more '$x$' it becomes a perfect cube.