Cube Root of Numbers

 

Definition

The cube root of any number say ‘a’, is the number ‘b’, which satisfies the equation given below:

b³ = a

This can be represented as:

a = ∛b

How to Find Cube Root of a Number

Cube root is the inverse process of calculating the cube of a number. It is denoted by the symbol ‘∛’. Let us see some examples here now.

To find the cube root of a number 27, we want a number which when multiplied thrice with itself shall give 27. We can write,

27 = 3 × 3× 3 = 3³

Taking cubic root on both the sides;

or ∛27 = ∛3³

Therefore, the cube-root of 27 is 3.

Please note that we will only consider the positive values cube roots of the natural numbers.

Cube Root of 2

Let us consider another example of number 2. Since 2 is not a perfect cube number. It is not easy to find the cube root of 2. With the help of the long division method, it is possible to find the cube roots for non-perfect cube numbers. The approximate value of the ∛2 is 1.260.

We can estimate the ∛2 by using the trick here.

Since, 2 = 1 x 1 x 2

Cube root of 2 is approximately equal to (1 + 1+2)/3 = 4/3 = 1.333..

Cube root of 4

Again 4 is a number, which is not a perfect cube. If we factorise it, we get:
4 = 2 x 2 x 1
Hence, we can see, we cannot find the cube root by simple factorisation here.
Again, if we use the shortcut method, we get:
∛4 is equal to (2+2+1)/3 = 1.67
The actual value of ∛4 is 1.587, which is approximately equal to 1.67.

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