A square has the same length and width. Which means, if the length is equal to 3 then the width should also be equal to 3. Therefore the area of square will be l*b i.e, 3*3 = 9. It can also be written as 3^{2} or called as 3 squared or 3 to the 2^{nd} power. A number that can be written as the square of another number is called a perfect square. We can find the exact square root of these numbers. **How to find square root of a number? **Check out the easy method given at BYJU’S.

## Finding Square Root of Number By Hand

Before proceeding further it is very important to clearly understand square numbers. Multiplication is the process of calculating one number by another. What does it mean when someone says the square of a number? To square a number means to multiply it by itself.

Example 1:

- 2 multiplied by 2 is equal to 4
- There is a shorter way to write 2 * 2. It is written as 2
^{2 } - It is also called 2 squared or 2 to the 2
^{nd}power

Example 2:

- 5 multiplied by 5 is equal to 25
- There is a shorter way to write 5 * 5. It is written as 5
^{2} - It is also called 5 squared or 5 to the 2
^{nd}power

A square root of a number is another number which when multiplied by itself gives back the original number. Methods to find square root: 1. The method of repeated subtraction 2. Prime factorization method 3. Long division method. There are certain square root rules that need to be followed while calculating the square root. The symbol used to denote the root of a number is called radical. Every radical has 3 parts: radical symbol, index, radicand.

## Examples

Example 1:

- Square root of 36 is 6
- Written as \( \sqrt{36} \) = 6 because 6 * 6 = 6
^{2 }= 36

Example 2:

- Square root of 25 is 5
- Written as\( \sqrt{25} \) = 5 because 5 * 5 = 5
^{2}= 25

## How to solve Square root equations?

Let us consider a radical equation, which has square root value in it.

√(x+1)=9

As we can see in the above equation, we have used radical under which a variable x is mentioned. Since, there is only one variable, therefore we will get the solution for x. Let us solve this equation now.

To remove the square we need to square the equations on both sides, i.e.,L.H.S and R.H.S.

Hence, we get;

[√(x+1)]^{2}=[9]^{2}

x+1 = 81

x = 81-1

x = 80.

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