##
**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 = 0

^{2}= 0 × 0 = 0
Square of 1 = 1

^{2}= 1 × 1 = 1
Square of 2 = 2

^{2}= 2 × 2 = 4
Square of 3 = 3

^{2}= 3 × 3 = 9
Square of 4 = 4

^{2}= 4 × 4 = 16
Square of 5 = 5

^{2}= 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 = √1

^{2}= 1
Square root of 4 = √4 = √2

^{2}= 2
Square root of 9 = √9 = √3

^{2}= 3
Square root of 16 = √16 =
√4

^{2}= 4
Square root of 25 = √25 =
√5

^{2}= 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*

*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.*

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