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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 twenty–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.