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.

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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.