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.

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:

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:

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:

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:

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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