How to find perfect square root?

There are two types of numbers:

Numbers which are a perfect square: Product of an integer with itself. For example, 9*9 = 81.

Numbers which are an imperfect square: Multiplying any number with itself. For example, 2.236*2.236 = 5.

Finding the square root of an imperfect square is a little more difficult than finding the square root of a perfect square number. 

A perfect square cannot have 2, 3, 7, or 8 in the unit’s digit.

If a perfect square ends with a 1, then the unit’s digit of its square root has to be either 1 or 9.

If a perfect square ends with a 4, then the unit’s digit of its square root has to be either 2 or 8.

If a perfect square ends with a 5, then the unit’s digit of its square root is definitely 5.

If a perfect square ends with a 6, then the unit’s digit of its square root has to be either 4 or 6.

If a perfect square ends with a 9, then the unit’s digit of its square root has to be either 3 or 7

To find out the number of digits in the answer.

The square root of a number with an odd number of digits (for example, 24563 has 5 digits i.e. odd) will have (n+1)/2 digits in the answer (in our example, (5+1)/2 = 3 digits in the answer). 

The square root of a number with an even number of digits (for example, 2456 has 4 digits i.e. even) will have n/2 digits in the answer (in our example, 4/2 = 2 digits in the answer). 

There are two methods known as Division method and Prime factorisation method of finding the square root of a number.

Eg:

Let us find the square root of 441. 

The prime factorization of 441 is 3 × 3 × 7 × 7. 

Make the pair and select one factor from each pair that gives 3 × 7 = 21. 

So, the square root of 441 = √441 = 21.