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Properties of Square Numbers

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Properties of Square Numbers:

Number Square Number Square
1 1 16 256
2 4 17 289
3 9 18 324
4 16 19 361
5 25 20 400
6 36 21 441
7 49 22 484
8 64 23 529
9 81 24 576
10 100 25 625
11 121 26 676
12 144 27 729
13 169 28 784
14 196 29 841
15 225 30 900
  • After observing the given table,
    All these numbers end with 0, 1, 4, 5, 6, or 9 at the unit place. None of these end with 2, 3, 7, or 8 at the unit’s place.
    So we can say that,
  • All square numbers end with 0, 1, 4, 5, 6, or 9 at the unit place. If a number has 2, 3, 7, or 8 in its units place then it is not a square number.

  • If a number has 1 or 9 in the units place, then it’s square ends in 1.

  • Square Number
    1 1
    81 9
    121 11
    361 19
    441 21
  • When a square number ends in 6, the number whose square it is will have either 4 or 6 in the unit’s place.
Square Number
16 4
36 6
196 14
256 16
  • Square numbers can only have an even number of zeros at the end.

    Square Number
    10000 100
    40000 200
    490000 700
    810000 900
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