Question

Find the square root of the following numbers by factorization.

(i) 196

(ii) 256

(iii) 10404

(iv) 1156

(v) 13225

Answer 1

(i) 196

196 = 2 × 2 × 7 × 7 

= 2 × 7 × 2 7 

196 = 14 × 14 

√196 = 14

(ii) 256

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 

256 = 16 × 16

(iii) 10404

10404 = 2 × 2 × 3 × 3 × 17 × 17 

= 2 × 3 × 17 × 2 × 17 

10404 = 102 × 102 

√10404 = 102

(iv) 1156

1156 = 2 × 2 × 17 × 17 

= 2 × 17 × 2 × 17 

1156 = 34 × 34

√1156 = 34

(v) 13225

13225 = 5 × 5 × 23 × 23 

= 5 × 23 × 5 × 23 13225 

= 115 × 115  

√13225 = 115