Perfect Square Definition

It is a whole number formed by multiplying a number by itself. In simple words, Perfect Square means the number that comes out by multiplying a single number two times. For Example, 16 is a perfect square because it is formed by multiplying 4 by 4.

A perfect square or square number has great significance in different fields of Mathematics, especially in Geometry. To find the Area of a square, the square number is used because you have to multiply a single number two times as the square has all sides with equal length.


Read about Geometry here.

Examples of Perfect Squares

4 = 2 x 2
9 = 3 x 3
16 = 4 x 4
25 = 5 x 5
36 = 6 x 6
49 = 7 x 7
64 = 8 x 8

The above-mentioned numbers are perfect squares because these are formed by multiplying the same number with itself.

Perfect Squares lower than 200

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196. 

Fun Facts about Perfect Square

  • A perfect square can’t be negative in any condition.
  • The square number always ends up with 0, 1, 4, 5, 6, and 9.
  • A number with an even number of zeros is always a perfect square while a number with the odd number of zeros can be a square of any number. For example, 100 and 400 are square numbers while 10 and 4000 are not perfect squares.
  • The Square Root of a perfect square number will always be an integer.


You can read about Adding Square Roots here.

How to check if a number is a perfect square or not?

The easiest way is to divide the number using prime factorization. If you are getting a pair of the same prime numbers as the divider of the number, it shows that the number is a perfect square. If you are getting an odd number of prime numbers and are unable to write them in pairs, it means that the number is not a perfect square.

Let us show you a few examples for better understanding.

Example 1:

Check whether 36 is a perfect square or not.


By prime factorization, we got the following numbers as the divider of this number.

36 = 2 x 2 x 3 x 3

We can see that prime numbers can be written in the form of pairs. It shows that 36 is a perfect square of the number.

Example 2:

Check whether 48 is a perfect square or not.


48 = 2 x 2 x 2 x 2 x 3 

We can see that “3” doesn’t exist in pair format which shows 48 is not a perfect square.


Can a perfect square be negative?

No, a square number can’t be negative because the square of two numbers is also a positive whole number.

What is the opposite of a perfect square?

The square root is the opposite of a square number or perfect square number.

Can we get the answer of a square number in decimal format?

A square number can’t give an answer in the decimal format. It should definitely show a whole number as its answer.