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Properties of Square Numbers

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Following table shows the squares of numbers from 1 to 20. 

Number Square Number Square
1 1 11 121
2 4 12 144
3 9 13 169
4 16 14 196
5 25 15 225
6 36 16 256
7 49 17 289
8 64 18 324
9 81 19 361
10 100 20 400

We observ that the square number ends with either 0 or 1 or 4 or 5 or 6 or 9 at its unit's place. We say that a square number always as will either 0 , 1 , 4 , 5,6 and 9T it's unit's place . 
The following square numbers end with digit 1.

Square  Number
1 1
81 9
121 11
361 19
441 21

We say that if a number has 1 or 9 in the units place, then it’s square ends in 1.
Let us consider square numbers ending in 6.

Square Number
16 4
36 6
196 14
256 16

when a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place.
Consider the following numbers and their squares.

We observe  that  a square number always has an even number of zeros at its end. A number with odd number of zeros is never a square of any number.

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