Find the square roots of the following numbers by the Prime Factorisation Method. 

(i) 729 (ii) 400 (iii) 1764

 (iv) 4096 (v) 7744 (vi) 9604 

(vii) 5929 (viii) 9216 (ix) 529 (x) 8100

Finding the square root of the following by prime factorization method : 

(i) Square root of 729 by prime factorization method.

Therefore, 

729= $3\times 3\times 3\times 3\times 3\times 3 =3^2\times 3^2\times 3^2$ 

$\sqrt{729}$ =$3\times 3\times 3 = 27$

$\sqrt{729}$ = 27

(ii)  Square root of 400 by prime factorization method.

400= $2\times 2\times 2\times 2\times 5\times 5 =2^2\times 5^2\times 2^2$ 

$\sqrt{400}$ =$2\times 2\times 5 = 20$

$\sqrt{400}$ = 20

(iii) Square root of 1764 by prime factorization method.

1764= $2\times 2\times 3\times 3\times 7\times 7 =2^2\times 3^2\times 7^2$ 

$\sqrt{1764}$ =$2\times 3\times 7 = 42$

$\sqrt{1764}$ = 42

(iv) Square root of 4096 by prime factorization method.

4096= $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2 =2^2\times 2^2\times 2^2\times 2^2\times 2^2\times 2^2$ 

$\sqrt{4096}$ =$2\times 2\times 2\times 2\times 2\times 2 = 64$

$\sqrt{4096}$ =  64

(v)  Square root of 7744 by prime factorization method.

7744= $2\times 2\times 2\times 2\times 2\times 2\times 11\times 11 =2^2\times 2^2\times 2^2\times {11}^2$ 

$\sqrt{7744}$ =$2\times 2\times 2\times 11 = 88$

$\sqrt{7744}$ =  88

(vi) Square root of 9604 by prime factorization method.

9604= $2\times 2\times 7\times 7\times 7\times 7 =2^2\times 7^2\times 7^2$ 

$\sqrt{9604}$ =$2\times 7\times 7 = 98$

$\sqrt{9604}$ =  98

(vii) Square root of 5929 by prime factorization method.

5929= $7\times 7\times 11\times 11=7^2\times {11}^2$ 

$\sqrt{5929}$ =$7\times 11 = 77$

$\sqrt{5929}$ =  77

(viii) Square root of 9216 by prime factorization method.

9216= $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3=2^2\times 2^2\times 2^2\times 2^2\times 2^2\times 3^2$ 

$\sqrt{9216}$ =$2\times 2\times 2\times 2\times 2\times 3 = 96$

$\sqrt{9216}$ =  96

(ix) Square root of 529 by prime factorization method.

529 = $23\times 23={23}^2$ 

$\sqrt{529}$ =$23$

$\sqrt{529}$ =  23

(x) Square root of 8100 by prime factorization method.

8100 = $2\times 2\times 3\times 3\times 3\times 3\times 5\times 5=2^2\times 3^2\times 3^2\times 5^2$ 

$\sqrt{8100}$ =$2\times 3\times 3\times 5$

$\sqrt{8100}$ =  90