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

(i) 729 (ii) 400

(iii) 1764 (iv) 4096

(v) 7744 (vi) 9604

(vii) 5929 (viii) 9216

(ix) 529 (x) 8100

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

729 = __3 × 3__ × __3 × 3__ × __3 × 3__

= 27

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

400 = __2 × 2__ × __2 × 2__ × __5 × 5__

= 20

(iii) The prime factorization of 1764 is as follows:

1764 = __2 × 2__ × __3 × 3__ × __7 × 7__

= 42

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

4096 = __2 × 2__×__2 × 2__×__2 × 2__×__2 × 2__×__2 × 2__×__2 × 2__

= 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__

= 2 * 2 * 2 * 11

= 88

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

9604 = __2 × 2__×__7 × 7__×__7 × 7__

= 2 * 7 * 7

= 98

(vii) The prime factorization of 5929 is as follows:

5929 = 11 × 11 × 7 × 7

= 11 * 7

= 77

(viii) 9216 can be factorized as follows:

9216 = __2 × 2__×__2 × 2__×__2 × 2__×__2 × 2__×__2 × 2__×__3 × 3__

= 2 * 2 * 2 * 2 * 2 * 396

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

529 = __23 × 23__

= 23

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

8100 = __2 × 2__×__5 × 5__×__3 × 3__×__3 × 3__

= 2 * 5 * 3 * 3

= 90

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