Below are the properties of Square :
1) When a perfect square is written as a product of its prime factors each prime factor will appear an even number of times.
2) The difference between the squares of two consecutive natural numbers is always equal to the sum of the natural numbers. Thus 41^2 - 40^2 = (40+41) = 81
3) The square of a number ending in 1, 5 or 6 also ends in 1, 5 or 6 respectively.
4) The value of a perfect square has to end in 1, 4, 5, 6, 9 or an even number of zeros.
5) If the units digit of the square of a number is 1, then the number should end in 1 or 9.
6) If the units digit of the square of a number is 4, then the units digit of the number is 2 or 8.
7) If the units digit of the square of a number is 9, then the units digit of the number is 3 or 7.
8) If the units digit of the square of a number is 6, then the units digit of the number is 4 or 6.
9) The square of a number is always non-negative.
10) Normally by squaring any number we increase the value of the number. The only integers for which this is not true are 0 and 1.
Further, for values between 0 to 1, squaring the number reduces the value of the number. For example 0.5^2 < 0.5