Question

How to know if a number is a perfect cube?

Answer 1

We often need to know or check if a number is a perfect cube in order to extract the cube root of the number within a very short time, especially in the competitive examinations.

The most straight forward method is to check through factorization. If the prime factors of a number are grouped in triples of equal factors, then that number is called a perfect cube.

In order to check whether a number is a perfect cube or not, we find its prime factors and group together triplets of the prime factors. If no factor is left out then the number is a perfect cube. However if one of the prime factors is a single factor or a double factor then the number is not a perfect cube.