**Important Concepts and Formulas on Squares and Square Roots**

1. When a number is multiplied by
itself, the product so obtained is called the square of that number.

2. A number whose square root is a whole
number is called a perfect square. For example 1, 4, 9, 16, 25, ... are perfect
squares.

3. Square numbers end in the digits 0,
1, 4, 5, 6 or 9.

4. Square numbers do not end in the
digits 2, 3, 7 or 8.

5. The square of an even number is
always even number and that of an odd number is always an odd number.

6. If the sum of squares of two numbers
is equal to the square of a third number then three numbers form a Pythagorean
triplet.

7. A square number cannot have odd
number of zeros at the end.

a. Repeated subtraction method

b. Prime factorization method

c. Long division method