Properties of Square Numbers

 1.  Square numbers from 1 to 20 in below table.

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

In above table, observe the square numbers. The ending digits of the square numbers are 0, 1, 4, 5, 6, and 9 at unit’s place, or all these numbers are end with 0, 1, 4, 5, 6, and 9.

In the above table no any number end with 2, 3, 7, or 8 at unit’s place.

Therefore, we can say that if a number ends in 0, 1, 4, 5, 6, and 9, then it must be a square number

2. The following table is square numbers, with end of digit 1.

Number	Square
1	1
9	81
11	121
19	361
21	441
29	841

In above table observe that if a number has 1 or 9 at the unit’s place, then its square number ends with 1.

3.  The following table is square numbers, with end of digit 6.

Number	Square
4	16
6	36
14	196
16	256
24	576
26	676

In above table observe, that if a number has 4 or 6 at the unit’s place, then its square number ends with 6.