Math: Perfect Square

How to guess if the number is a perfect square:

1. A perfect square will always have a unit digit of 1, 4, 5, 6, 9 or 0.

2. A perfect square will always have a 10′s digit which is even, Except when the unit digit of a perfect square is 6, in which case the 10’s digit is always odd.

3. If the unit digit of a perfect square is any other number, then the 10’s digit of a perfect square is always even.

4. A perfect square ending in 5, will always have 2 as the 10’s digit.

5. A perfect square ending in 0, will always have 0 as the 10’s digit ( even number of ending 0’s) .

 A number cannot be an exact or perfect square if:

- it ends in 2, 3,7 or 8

- it terminates in an odd number of zeros

- its last digit is 6 but its penultimate (tens) digit is even

- its last digit is not 6 but its penultimate (tens) digit is odd

- its last digit is 5 but its penultimate (tens) digit is other than 2

- its last 2 digits are not divisible by 4 if it is even number