# Square and Square Roots ## Square and Square Roots

### Square Numbers

A number obtained by multiplying any number with the same number is called a square number. It is represented by giving the power 2 to the multiplicand.

For example,
Square of 0 = 02 = 0 × 0 = 0
Square of 1 = 12 = 1 × 1 = 1
Square of 2 = 22 = 2 × 2 = 4
Square of 3 = 32 = 3 × 3 = 9
Square of 4 = 42 = 4 × 4 = 16
Square of 5 = 52 = 5 × 5 = 25 and so on.

Note: Square of whole numbers i.e 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, … etc are called perfect square numbers.

Square numbers can be calculated simply by multiplying the number with same number.

For example,
Square of 15 = 15 × 15 = 225

### Square Root

Square number and square root are correlated. When we multiply two same numbers we get a square number, and that multiplicand of the square number is called a square root. It is represented by giving power ½ to the square number or using radical sign of square root .

For example,
Square root of 1 = √1 = √12 = 1
Square root of 4 = √4 = √22 = 2
Square root of 9 = √9 = √32 = 3
Square root of 16 = √16 = √42 = 4
Square root of 25 = √25 = √52 = 5 and so on.

### Square root can be calculated by using the following methods:

a.    Prime factorization method
b.    Division method

#### Prime Factorization Method

In this method we factorize the number into its prime factors and form the power of 2.
For example,

#### Division Method

For division method the digits of the given number are separated by a bar from right to left making a pair. The process of finding the square root of 625 by division method is shown below:
The square root of 625 = 25

### Workout Examples

Example 1: Find the square root of 7056 by prime factorization method.

Solution: Here,

Example 2: Find the square root of 60516 by division method.

Solution: Here,
The square root of 60516 = 246

You can comment your questions or problems regarding the square numbers and square roots here.