A natural number m is called a perfect square number if it can be expressed as where n is also a natural number. For example, 4 is a perfect square number because it is a natural number and it can be expressed as and 2 is also a natural number.
Can we write all the perfect square numbers from 1 to 100. Certainly, we can...
So, all the perfect square numbers from 1 to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
Similarly, we can keep writing perfect square numbers greater than 100.
, , , , , , , , , and so on....
Properties of Perfect Square Numbers:

 Note that all the perfect square numbers end with 0, 1, 4, 5, 6 or 9. Can you think of any perfect square number which ends with 2, 3, 7 or 8? There is no such number. Note that perfect square numbers end with 0, 1, 4, 5, 6 or 9 but every number which ends with 0, 1, 4, 5, 6 or 9 is not a perfect square numbers. For example, 11 is not a perfect square number and it ends with 1. It cannot be expressed as where n is a natural number. Can you write five more numbers which end with 0, 1, 4, 5, 6 or 9 and are not perfect square numbers?
 2n nonperfect square numbers lie between two consecutive perfect square numbers. Please go through article for more details.
 Every nth perfect square number can be expressed as sum of first n odd numbers. For example, 2nd perfect square number which is 4 can be expressed as sum of first two odd numbers (1+3=4). Similarly, 5th perfect square number which is 25 can be expressed as sum of first 5 odd numbers (1+3+5+7+9=25). This point can also be rewritten as sum of first n odd numbers is equal to . Please read the article for better understanding.