Find the square roots of the following numbers by the Prime Factorization Method

(i) The prime factorization of 729 is as follows:

729 = 3 × 3 × 3  × 3 × 3  × 3

√729 = 3 × 3 × 3

= 27

(ii)The prime factorization of 400 is as follows:

400 = 2 × 2 × 2 × 2 × 5 × 5

√400 = 2 × 2 × 2 × 2 × 5 × 5

=20

(iii)Theprimefactorizationof1764isasfollows:

1764 = 2×2×3×3×7×7

 √1764 = 2 × 3 ×  7

= 42

(iv)The prime factorization of 4096 is as follows:

4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 

√4096 = 2 * 2 *  2 * 2 * 2 * 2

= 64

(v)The prime factorization of 7744 is as follows:

7744 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11

√7744 = 2 * 2 * 2 * 11

= 88

(vi)The prime factorization of 9604 is as follows:

9604 = 2 × 2 × 7 × 7 × 7 × 7

√9604 = 2 * 7 * 7

= 98

(vii)Theprimefactorizationof5929isasfollows:

5929=11×11×7×7

 √5929 = 11 * 7

= 77

(viii) 9216 can be factorized as follows:

9216 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

 √9216 = 2 * 2 *  2 * 2 * 2 * 396

(ix) The prime factorization of 529 is as follows:

529 = 23 × 23

 √529 = 23

(x)The prime factorization of 8100 is as follows:

8100 = 2 × 2 × 5 × 5 × 3 × 3 × 3 × 3

 √8100 = 2 * 5 * 3 * 3

= 90