FINDING SQUARE ROOT BY PRIME FACTORIZATION METHOD

In the page "finding square root by prime factorization method",  we are going to learn how to find square root of a number.

What is square root?

The square root of a number is the value such that,when a number multiplied by itself,for example

   3 x 3 = 9

3 is square root of 9.

The symbol of square root:

A square root is written with a radical symbol

and the number or expression inside the radical symbol is called the radicand.

Methods to find square root of perfect square

(i) Prime factorization 

(ii) Long division method

How to find the square root of a number using prime factorization

  • Using this method, first we have to split the given number into prime factors.
  • Write those prime factors inside the radical sign instead of the given number.
  • Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.
  • Multiply the numbers which have come out from the radical sign.

Examples of finding square root by prime factorization method

Question 1 : 

Find square root of 324 by prime factorization

Solution :

Step 1 :

Split 324 into prime factors 

Step 2 :

324  =  √2 x 2 x 3 x 3 x 3 x 3 

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

Hence, square root of 324 is 18.

Let us see the next example on "Finding square root by prime factorization method"

Question 2 : 

Find square root of 625 by prime factorization

Solution :

Step 1 :

Split 625 into prime factors 

Step 2 :

√625  =  √5 x 5 x 5 x 5

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  5 x 5

  =  25

Hence, square root of 625 is 25.

Let us see the next example on "Finding square root by prime factorization method"

Question 3 : 

Find square root of 4096 by prime factorization

Solution :

Step 1 :

Split 625 into prime factors 

Step 2 :

√4096  =  √2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 3 :

Take one common number from the radical

  =  2 x 2 x 2 x 2

  =  64

Hence, square root of 4096 is 64.

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Question 4 : 

Find square root of 400 by prime factorization

Solution :

Step 1 :

Split 400 into prime factors 

Step 2 :

√400  =  √2 x 2 x 2 x 2 x 5 x 5

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  2 x 2 x 5

  =  20

Hence, square root of 400 is 20.

Let us see the next example on "Finding square root by prime factorization method"

Question 5 : 

Find square root of 144 by prime factorization

Solution :

Step 1 :

Split 144 into prime factors 

Step 2 :

√144  =  √2 x 2 x 2 x 2 x 3 x 3

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  2 x 2 x 3

  =  12

Hence, square root of 144 is 12.

Let us see the next example on "Finding square root by prime factorization method"

Question 6 : 

Find square root of 1024 by prime factorization

Solution :

Step 1 :

Split 1024 into prime factors 

Step 2 :

√1024  =  √2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  2 x 2 x 2 x 2 x 2

  =  32

Hence, square root of 1024 is 32.

Let us see the next example on "Finding square root by prime factorization method"

Question 7 : 

Find square root of 256 by prime factorization

Solution :

Step 1 :

Split 256 into prime factors 

Step 2 :

√256  =  √2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  2 x 2 x 2 x 2 

  =  16

Hence, square root of 256 is 16.

Let us see the next example on "Finding square root by prime factorization method"

Question 8 : 

Find square root of 2025 by prime factorization

Solution :

Step 1 :

Split 2025 into prime factors 

Step 2 :

√2025  =  √5 x 5 x 3 x 3 x 3 x 3 

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  5 x 3 x 3

  =  45

Hence, square root of 2025 is 45.

Question 9 : 

Find square root of 36 by prime factorization

Solution :

Step 1 :

Split 36 into prime factors 

Step 2 :

√36  =  √2 x 2 x 3 x 3

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  2 x 3 

  =  6

Hence, square root of 36 is 6.

Question 10 : 

Find square root of 3136 by prime factorization

Solution :

Step 1 :

Split 3136 into prime factors 

Step 2 :

√3136  =  √2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 

Step 3 :

Inside the radical sign, if the same number is repeated twice, take one number out of the radical sign.

  =  2 x 2 x 2 x 7 

  =  56

Hence, square root of 3136 is 56.

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