Finding Square root using prime factorization method

Procedure to find square root using prime factorization method 

  • Write the prime factors of the given number 
  • Make pairs of the equal factors 
  • Write one factor corresponding to each pair 
  • Multiply the obtained factors

Q.1 Find the square root of 256 using the prime factorization method.

Solution: Prime factorization of 256

256=2×2×2×2×2×2×2×2

Make pairs 

256=2×2×2×2×2×2×2×2

√256=√2×2×2×2×2×2×2×2

√256=2×2×2×2

√256=16 

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=2×2×3

√144=12 

Q.3 Find the square root of 1024 using the prime factorization method.

Solution: 

Prime factorization of 1024

1024=2×2×2×2×2×2×2×2×2×2

1024=2×2×2×2×2×2×2×2×2×2

√1024=√2×2×2×2×2×2×2×2×2×2

√1024=2×2×2×2×2

√1024=32 

Q.4 Find the square root of 4096 using the prime factorization method.

Solution: 

Prime factorization of 4096

4096=2×2×2×2×2×2×2×2×2×2×2×2

Sorry ! ,there is one more 2 in the factorization which i forgot to mention 

4096=2×2×2×2×2×2×2×2×2×2×2×2

√4096=√2×2×2×2×2×2×2×2×2×2×2×2

4096=2×2×2×2×2×2

4096=64

Q.5 Find the square root of 784 using the prime factorization method.

Solution: 

prime factorization of 784

784=2×2×2×2×7×7

Make pairs 

784=2×2×2×2×7×7

√784=√2×2×2×2×7×7

√784=2×2×7

√784=28 

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