**Unit digit of Perfect Squares**

**Properties regarding Unit Digit of Perfect Square**

Squares: There is a definite relationship between the unit digits when square of a number is considered, we will see that one by one.

– If unit digit of a perfect square is 1 then ten’s digit has to be Even

E.g. 81, 121, 441, 961 all are Perfect Square having unit digit 1 and tens digit is even.

– If unit digit of a number is 2 then it can’t be a perfect square.

– If unit digit of a number is 3 then it can’t be a perfect square.

– If unit digit of a perfect square is 4 then ten’s digit has to be Even.

E.g. 64, 144, 484 all are Perfect Square having unit digit 4 and tens digit is even.

– If unit digit of a perfect square is 5 then ten’s digit has to be 2

E.g. 25, 225, 625,1225 all are Perfect Square having unit digit 5 and tens digit is 2.

– If unit digit of a perfect square is 6 then ten’s digit has to be Odd. e.g. 256, 576, 676, 1296 etc.

– If unit digit of a number is 7 & 8 then it can’t be a perfect square

– If unit digit of a perfect square is 9 then ten’s digit has to be Even.

E.g. 49, 169, 529 all are Perfect Square having unit digit 9 and tens digit is even.

– If unit digit of a perfect square is 0 then ten’s digit has to be 0.

E.g. 100,400,900 all are Perfect Square having unit digit 0 and tens digit is 0.

– If a number ends with 2, 3, 7 or 8 then it can’t be perfect square.

-Square of any natural number has last two digits same as that of last two digits of squares of first twentyâ€“five natural numbers. For example if we calculate square of

88 we get 7744. You can notice that last two digits are 44, which are same as last two digits of the square of 12 i.e. 144.

the square of first 20 natural numbers are

1=1

2=4

3=9

4=16

5=25

6=36

7=49

8=64

9=81

10=100

11=121

12=144

13=169

14=196

15=225

16=256

17=289

18=324

19=361

20=400

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