What is cube root?

A cube root of a number is a value that, when multiplied by itself three times, gives the original number.

For example:

• The cube root of 8 is 2, because 2×2×2=8
• The cube root of 27 is 3, because 3×3×3=27

Mathematically, the cube root of a number x is written as:

x³  or  ³√x

Concept of Cube Root by Prime Factorization

Cube root by prime factorization is a method to determine the cube root of a number by breaking it down into its prime factors.

Concept:

1. Prime Factorization: Express the given number as a product of its prime factors.
2. Grouping in Triplets: Arrange the prime factors in groups of three.
3. Extracting Cube Root: Take one factor from each triplet and multiply them to get the cube root.

Key Idea:

• A number is a perfect cube if all its prime factors appear in multiples of three.