Square root Prime factorization

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.

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 = 2 x 11 = 22 Therefore, √484 = 22

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 = 2 x 3 x 11 = 66 Therefore, √4356 = 66

2. Find the square root of 12.25 by prime factorization method. Solution: Step 1: First we need to convert 12.25 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 = 5 x 7 = 35 Therefore, √1225 = 35

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 = 2 x 5 = 10 Therefore, √100 = 10

Try These Evaluate √625 Evaluate √4761 Evaluate √110.25