# HOW TO CHECK WHETHER THE GIVEN NUMBER IS PERFECT SQUARE OR NOT

## About "How to check whether the given number is perfect square or not"

How to check whether the given number is perfect square or not ?

Here we are going to see How to check whether the given number is perfect square or not.

Perfect Square :

The numbers 1, 4, 9, 16, 25, g are called perfect squares or square numbers as

1 = 12, 4 = 22, 9 = 32, 16 = 42 and so on.

A number is called a perfect square if it is expressed as the square of a number.

We may observe the following properties through the patterns of square numbers.

Property 1 :

In square numbers, the digits at the unit’s place are always 0, 1, 4, 5, 6 or 9. The numbers having 2, 3, 7 or 8 at its units' place are not perfect square numbers.

Property 2 :

(i)  If a number has 1 or 9 in the unit's place then its square ends in 1.

 Number1911 Square181121

(ii)  If a number has 2 or 8 in the unit's place then its square ends in 4.

 Number2812 Square464144

(iii)  If a number has 3 or 7 in the unit's place then its square ends in 9.

 Number3713 Square949169

(iv)  If a number has 4 or 6 in the unit's place then its square ends in 6.

 Number4614 Square1636196

(v)  If a number has 5 in the unit's place then its square ends in 5.

 Number51525 Square25225625

(v)  If a number has 5 in the unit's place then its square ends in 5.

 Number51525 Square25225625

Property 3 :

When a number ends with ‘0’ , its square ends with double zeros.

Let us consider the following examples,

102  =  100, 202  =  400

1002  =  10000, 2002  =  40000

Property 4 :

If a number ends with odd number of zeros then it is not a perfect square.

Let us consider the examples,

Check if 100 is a perfect square.

100 is a perfect square. Because it has even number of zeroes.

100  =  10 ⋅ 10  =  102

(ii)  81000  =  81 ⋅ 10 ⋅ 100

=  92⋅ 10 ⋅ 102

Hence 81000 is not a perfect square. Because it has odd number of zeroes.

Property 5 :

(i) Squares of even numbers are even.

(ii) Squares of odd numbers are odd.

Let us look into some example problems to understand the above concepts.

Example 1 :

By observing the unit’s digits, which of the numbers 3136, 867 and 4413 can not be perfect squares?

Solution :

Since 6 is in units place of 3136, there is a chance that it is a perfect square.

867 and 4413 are surely not perfect squares as 7 and 3 are the unit digit of these numbers.

Example 2 :

Just observe the unit digit and state if the given number is perfect square or not.

9348

Solution :

In square numbers, the digits at the unit’s place are always 0, 1, 4, 5, 6 or 9.

Since the unit digit is 8, it is not a perfect square.

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