take a number then divide by 5 then and the multiply the result with the original number and then take this result and divide by 2 and then multiply with 10 and finally you have the square of the original number. this is just the beauty of maths

 

You can also find the square of the any number as a quadratic sequence 

furthermore you can add the progressing odd number to the progressing square number to find the next square number like this

 

0 + 1 (the first odd number) = 1 = 1^2

1 + 3 (the second odd number) = 4 = 2^2

4 + 5 (the third odd number) = 9 = 3^2

9 + 7 (the third odd number) = 16 = 4^2

16 + 9 (the third odd number) = 25 = 5^2

And this goes on…

 

Another one pattern could be looked below

 

2^2 = 4                4^2 = 16

2^3 = 8                                           8^2 = 64

2^4 = 16              4^3 = 64