1. Square root Prime factorization

2. Square Root - Prime Factorization Method
To find the square root using the prime factorization method
Step I:  Factorize into prime factors.
Step II:  Make pairs of factors.
Step III:  Take out one factor from each pairs.

3. 1. Find the square root of 484 by prime factorization method.
Solution:
Step 1: Factorize into prime factors, we get
Step 2: Make pairs of factors
Step 3: Take out one factors from each pair
484 = 2 x 2 x 11 x 11
√484 = x = 22
Therefore, √484 = 22

4. 2. Find the square root of 4356 by prime factorization method.
Solution:
Step 1: Factorize into prime factors, we get
Step 2: Make pairs of factors
Step 3: Take out one factors from each pair
4356 = 2 x 2 x 3 x 3 x 11 x 11
√ 4356 = x x = 66
Therefore, √4356 = 66

5. 2. Find the square root of 12.25 by prime factorization method.
Solution:
Step 1: First we need to convert into whole number
We have 2 decimal points
We have to multiply and divide it by 100
Steps to find square root of 1225
Step 1: Factorize into prime factors, we get
Step 2: Make pairs of factors
Step 3: Take out one factors from each pair
1225 = 5 x 5 x 7 x 7
√ 1225 = x = 35
Therefore, √1225 = 35

6. Steps to find square root of 100
Step 1: Factorize into prime factors, we get
Step 2: Make pairs of factors
Step 3: Take out one factors from each pair
100 = 2 x 2 x 5 x 5
√ 100 = x = 10
Therefore, √100 = 10

7. Try These
Evaluate √625
Evaluate √4761
Evaluate √110.25