Finding square root using prime factorization method part 2

 

Q.1 Find the square root of 625 using the prime factorization method 

Solution: 

Prime factorization of 625

625=5×5×5×5 

Make pairs

625=5×5×5×5 

√625=√5×5×5×5 

√625=5×5

√625=25 

Q.2 Find the square root of 144  using the prime factorization method 

Solution: 

prime factorization of 144

144=2×2×2×2×3×3

Make pairs 

144=2×2×2×2×3×3

√144=√2×2×2×2×3×3

√144=2×3×2

√144=12

Q.3 Find the square root of 400 using the prime factorization method 

Solution: 

Prime factorization of 400

400=2×2×2×2×5×5

Make pairs 

400=2×2×2×2×5×5

√400=√2×2×2×2×5×5

√400=2×2×5

√400=20

Q.5 Find the square root of 5929 using the prime factorization method

Solution: 

Prime factorization of 5929

5929=7×7×11×11

Make pairs 

5929=7×7×11×11

√5929=√7×7×11×11

5929=7×11

5929= 77 

Q.6 Find the square root of 9604 using the prime factorization method 

Solution: Prime facorization of 9604 9604=2×2×7×7×7×7

Make pairs 

9604=2×2×7×7×7×7

√9604=√2×2×7×7×7×7

√9604=2×7×7

√9604=98

Q.7 Find the square root of 729 using the prime factorization method 

Solution: prime factorization of 729 729=3×3×3×3×3×3

Make pairs 

729=3×3×3×3×3×3

√729=√3×3×3×3×3×3

√729=3×3×3

√729=27 

Check 

 

 

 

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