Question

How can we find the perfect cube and what 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.

Examine if (i) 106480 and (ii) 19683 are perfect cubes.

106480

One prime factor 2 and the prime factor 5 are not parts of a triplet so 106480 is not a perfect cube.

Is 19683 a perfect cube?

19683

Since the prime factor 3 forms three triplets so 19683 is a perfect cube.