Cube Roots

Cube root of number is a value which when multiplied by itself thrice or three times produces the original value. For example, the cube root of 27, denoted as 3√27, is 3, because when we multiply 3 by itself three times we get 3 x 3 x 3 = 27 = 33. So, we can say, the cube root gives the value which is basically cubed. Here, 27 is said to be a perfect cube. From the word, cube root, we can understand what is the root of the cube. It means which number caused the cube present under the root. Usually, to find the cubic root of perfect cubes, we use the prime factorisation method. 

Cube Root Symbol

The cube root symbol is denoted by ‘3√’. In the case of square root, we have used just the root symbol such as ‘√’, which is also called a radical. Hence, symbolically we can represent the cube root of different numbers as: Cube root of 5 = 3√5 Cube root of 11 = 3√11 and so on

Cube Root Formula

As we already know, the cube root gives a value which can be cubed to get the original value. Suppose, cube root of ‘a’ gives a value ‘b’, such that;
3√a = b This formula is only possible if and only if; a = b3
This formula is useful when we find the cubic root of perfect cubes.

But for imperfect cubes, we cannot evaluate the cube root this easily. 

How to Find Cube Root?

To find the cubic root of a number easily, we can use the prime factorisation method. By evaluating the prime factors we can pair similar digits in a group of three and take them out as a single digit from the cubic root. Let us take an example of finding the cube root of 8. By factoring 8, we get; 8 = 2 x 2 x 2 8 = 23
Now, if we take the cubic root both the sides, then the cube of 2 cancels the cubic root. Hence, we get the value of 3√8 Therefore,
3√8 = 2