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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