In this chapter we will learn about the concept of square root and the method to calculate it.

## What does square root mean ?

Let ” a ” be the positive integer.

On squaring the number, we get \mathtt{a^{2}} .

Now, if we take square root of number \mathtt{a^{2}} , we will get back the original number ” a “

Hence, square root is the inverse operation of squaring the number.

### How to represent square root of number ?

If you want to represent square root of any number, place ” \mathtt{\sqrt{}} ” sign above that number.

**For example;**

square root of 16 ⟹ \mathtt{\sqrt{16}}

square root of 25 ⟹ \mathtt{\sqrt{25}}

## How to find square root of number ?

Here we will learn to find square root of perfect square.

**Follow the below steps;**

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

(b) **Arrange all the factor in pair of two**.

This means that all the factors will have exponent of 2.

(c) **Remove all the exponents and simply multiply the factors** to get the square root.

I hope you understood the above concept, let us now solve some problems.

**Example 01**

Find the square root of 100

**Solution**

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

**(b) Arrange all factor in pair of two.**

The above factorization can be expressed as;

\mathtt{100\ =2^{2} \times 5^{2}}

All the factors have exponent 2 means that the given number is a perfect square.**(c) Remove the exponent and multiply the numbers to get square root**.

Square root 100 ⟹ 2 x 5

Square root 100 ⟹ 10

Hence, **10 is the square root of **100.

It means that if we multiply 10 by itself we get 100.

**Example 02**

Find the square root of 256

**Solution**

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

**(b) Arrange all factor in pair of two.**

The above factorization can be expressed as;

\mathtt{256\ =2^{2} \times 2^{2} \times 2^{2} \times 2^{2}}

All the factors have power 2, this mean that the above number is perfect square.**(c) To get the square root, remove the exponents and multiply the numbers.**

Square root 256 ⟹ 2 x 2 x 2 x 2

Square root 256 ⟹ 16

Hence, **16 is the square root of number 256.**

**Example 03**

Find the square root of 324

**Solution**

Follow the below steps;

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

**(b) Now form a pair of two of all the factors.**

The prime factorization can be represented as;

\mathtt{324\ =2^{2} \times 3^{2} \times 3^{2}}

Since all the factors have exponent of two, the number 324 is a perfect square.

**(c) To get the square root, remove the exponents and multiply the numbers.**

Square root 324 ⟹ 2 x 3 x 3

Square root 324 ⟹ 18

Hence, **18 is the square root of number 324.**

This mean that if we multiply 18 by itself, we get 324.

**Example 04**

Find the square root of 2025

**Solution****(a) Do the prime factorization**

**(b) Arrange the factors in pair of two**

The above factorization can be expressed as;

\mathtt{2025\ =3^{2} \times 3^{2} \times 5^{2}}

Since, all the factors have exponent two, the number 2025 is a perfect square.

**(c) To get the square root, remove the exponents and multiply the number.**

Square root 2025 ⟹ 3 x 3 x 5

Square root 2025 ⟹ 45

Hence, **45 is the square root of number 2025.**

**Example 05**

Find the square root of 288

**Solution**

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

The above factorization can be represented as;

\mathtt{288\ =2^{2} \times 2^{2} \times 3^{2} \times 2}

Here, the factor 2 at the end has exponent 1.

From the above factorization, we can see that when we form pair of two, the factor 2 is left out. Hence, the number is not a perfect square.

We cannot calculate the **square root of non-perfect square using this method.**