Perfect Square
Square of a number is the number which is obtained by multiplying the number by itself. If N is a number, then the square of it is N × N = N2.
For example, the square of 2 is 22 = 2 × 2 = 4.
The square (the shape) has all its sides equal. As we know, the area of a square is equal to the square of its side, i.e.,
Area of Square = Side × Side = Side2
In the same way, the square numbers are the product of a number by itself.
And Square of a number = N × N = N2
Square of Even Numbers
From numbers 1 to 50 there are a total of 25 even numbers. As we know, even numbers can be represented in the form of 2n, where n = 1,2,3,4,5,…
Hence, the square of even numbers can be written as;
(2n)2 = 4n2
If n=1, then; 4n2 = 4(1)2 = 4
If n=2, then; 4(2)2 = 4.2.2 = 16
We can see, in this way, we can generate squares of all the even numbers.
Square of Odd Numbers
Likewise even numbers, there are a total of 25 odd numbers from 1 to 50. The odd numbers are represented in the form of 2n+1, where n = 0,1,2,3,4,5,….
Hence, the square of odd numbers can be written as;
(2n+1)2 = 4n2+4n+1 = 4n(n+1)+1
If n=1, then; 4(1+1)+1=4.2+1 = 9
If n=2, then; 4.2(2+1)+1 = 8(3) = 25
And so on.
In this way, the squares of all odd numbers can be determined.
How to Square A Number?
To square a number: multiply it by itself.
Example: What is 3 squared?
| 3 Squared | = |  |
= 3 × 3 = 9 |
“Squared” is often written as a little 2 like this:
This says “4 Squared equals 16”
(the little 2 says the number appears twice in multiplying)
Squares From 02 to 62
| 0 Squared | = | 02 | = | 0 × 0 | = | 0 |
| 1 Squared | = | 12 | = | 1 × 1 | = | 1 |
| 2 Squared | = | 22 | = | 2 × 2 | = | 4 |
| 3 Squared | = | 32 | = | 3 × 3 | = | 9 |
| 4 Squared | = | 42 | = | 4 × 4 | = | 16 |
| 5 Squared | = | 52 | = | 5 × 5 | = | 25 |
| 6 Squared | = | 62 | = | 6 × 6 | = | 36 |