PROPERTIES

A number ending with odd number of zeroes is never a perfect square.

Squares of even numbers are always even.

Squares of odd numbers are always odd.

The numbers ending with 2,3,7 and 8 are never perfect squares.

The square of a number other than 0 and 1, is either a multiple of 3 or exceeds the multiple of 3 by 1.

The square of a number other than 0 and 1, is either a multiple of 4 or exceeds a multiple of four by 1.