In this post we will learn about the concept of cube root and the method to find cube root of any number.

## What is Cube root ?

Let ” a ” be positive integer.

When we take cube of the number, we get \mathtt{( a)^{3}}

Now, if we take the cube root of number \mathtt{( a)^{3}} , we get the original number a.

Hence, **cube root is an inverse operation of cubing the number**.

### How to represent cube root of number ?

If you want to find cube root of any number, place \mathtt{\sqrt[3]{}} sign above that number.

**For example**;

cube root of 8 ⟹ \mathtt{\sqrt[3]{8}}

cube root of 125 ⟹ \mathtt{\sqrt[3]{125}}

## How to find cube root of number ?

Here we will learn to find the cube root of **perfect cube**.

Follow the below steps;

(a) Do **prime factorization** of number

(b) Arrange the factors in **pair of three**.

For perfect cube, we will get all the factors raised to the power of three.

(c) **Remove the powers and multiply the factors**, you will get the cube of number.

I hope you understood the above process, let us solve some examples for practice.

**Example 01**

Find cube root of number 216

**Solution**

Follow the below steps;**(a) Do the prime factorization**

The prime factorization can be expressed as;

\mathtt{216\ =2^{3} \times 3^{3}}

**(b) Arrange the factors in pair of three.**

\mathtt{216\ =2^{3} \times 3^{3}}

In the above prime factorization, factors 2 & 3 are arranged in pair of three since both the factors have same power 3.

This tells that the number 216 is a perfect cube.

(c) Now** remove the power and multiply the existing factors**.

Cube root of 216 ⟹ 2 x 3

Cube root of 216 ⟹ 6

Hence,** 6 is the cube root of number 216**.

This means that if you multiply 6 by itself thrice, you will get 216.

**Example 02**

Find the cube root of 1331

**Solution**

(i) Do the **prime factorization**

The above factorization can be expressed as;

\mathtt{1331\ =11^{3}} **(ii) Arrange the factor with power of three**

\mathtt{1331\ =11^{3}}

In the above factorization, we get factor 11 with power 3. Hence, the number 1331 is a perfect cube.**(iii) Remove the power and multiply the factors**

cube root of 1331 = 11

Hence, **cube of 1331 is 11**.

**Example 3**

Find the cube root of number 8000

**Solution**

Follow the below steps;**(i) Do the prime factorization**

The prime factorization is expressed as;

\mathtt{8000\ =2^{3} \times 2^{3} \times 5^{3}}

**(ii) Arrange all the factors in pair of three**.

In the above factorization calculation, you can observe that;

Factor 2 ⟹ form pair of three

Factor 2 ⟹form pair of three

Factor 5 ⟹ form pair of three

\mathtt{8000\ =2^{3} \times 2^{3} \times 5^{3}}

Since all factors have power 3, the number 8000 is a perfect cube.

**(iii) Remove the power and multiply the factors**.

Cube root of 8000 ⟹ 2 x 2 x 5

Cube root of 8000 ⟹ 20

Hence, **cube root of number 8000 is 20**.

**Example 04**

Find the cube root of 9261

**Solution****(i) Calculate the prime factorization**

The above factorization can be expressed as;

\mathtt{9261\ =3^{3} \times 7^{3}}

**(ii) Arrange all factors in pair of three**

Note that in above factorization both the factors 3 and 7 form pair of three.

Factor 3 ⟹ form pair of three

Factor 7 ⟹form pair of three

\mathtt{9261\ =3^{3} \times 7^{3}}

Since all the factors have power of three, the number 9261 is a perfect cube.**(iii) To find cube root, remove the power and simply multiply the factors.**

cube root 9261 ⟹ 3 x 7

cube root 9261 ⟹ 21

Hence, **cube root of number 9261 is 21.**

**Example 5**

Find the cube root of 128

**Solution**

(i) **Do the prime factorization**

The above factorization can be expressed as;

\mathtt{128\ =2^{3} \times 2^{3} \times \ 2}

**(ii) Arrange factors in pair of three**

\mathtt{128\ =2^{3} \times 2^{3} \times \ 2}

From the above expression, **note that all factors do not form pair of three**. This means that the number **128 is not a perfect cube**.

To find the cube root, the number has to be perfect cube. Hence, we stop the process at this point.