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.

Number

1

9

11

Square

1

81

121

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

Number

2

8

12

Square

4

64

144

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

Number

3

7

13

Square

9

49

169

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

Number

4

6

14 

Square

16

36

196

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

Number

5

15

25 

Square

25

225

625

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

Number

5

15

25 

Square

25

225

625

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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