LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FINDING SQUARE ROOT BY PRIME FACTORIZATION METHOD

__Finding Square Root By Prime Factorization __

**Step.1) We have to write the number as a product of prime
factors.**

**Step.2) Make pairs of
equal prime factors**

**Step.3) Take one factor from each pair and multiply them.**

**We can also express the number as a product of powers of
prime factors, taking half of each index and then finding the product of the
factors will give the square root**

**There are some example are given below for better
understanding –**

**1)
Find the square root of 5625**

**So, 5625 =
5 X 5 X 5 X 5 X 3 X 3 **

** = ( 5 X 5 ) X ( 5 X 5 ) X ( 3 X 3 )**

** √5625 = 5 X 5
X 3 = 75 **

** On the other way –**

** 5625 = 5⁴ X 3²
**

** So, √5625 = 5² X 3
= 25 X 3 = 75 **

** 2) Find the square
root of 19600**

**So, 19600 =
5 X 5 X 4 X 4 X 7 X 7**

** = ( 5 X 5 ) X ( 4 X 4 ) X ( 7 X 7 )**

** √19600 = 5 X
4 X 7 = 140 **

** On the other
way –**

** 19600 = 5²
X 4² X 7²**

** So, √19600 = 5
X 4 X 7 = 140 **

**3) Find the square root of 48400**

**So, 48400 = 5 X 5 X 4 X 4 X 11 X 11 **

** = ( 5 X 5 ) X ( 4 X 4 ) X ( 11 X 11 )**

** √48400 = 5 X
4 X 11 = 220 **

** On the other
way –**

** 48400 = 5²
X 4² X 11²**

** So, √48400 = 5
X 4 X 11 = 220**