Find the square root of each of the following by prime factorization.
(i) 441 (ii) 196
(iii) 529 (iv) 1764
(v) 1156 (vi) 4096
(vii) 7056 (viii) 8281
(ix) 11664 (x) 47089
(xi) 24336 (xii) 190969
(xiii) 586756 (xiv) 27225
(xv) 3013696
(i) 441
441 = 32 × 72
= 3 × 7
= 21
(ii) 196
196 = 22 × 72
= 2 × 7
= 14
(iii) 529
529 = 232
= 23
(iv) 1764
1764 = 22 × 32 × 72
= 2 × 3 × 7
= 42
(v) 1156
1156 = 22 × 172
= 2 × 17
= 34
(vi) 4096
4096 = 212
= 26
= 64
(vii) 7056
7056 = 22 × 22 × 212
= 2 × 2 × 21
= 84
(viii) 8281
8281 = 912
= 91
(ix) 11664
11664 = 22 × 22 × 32 × 32 × 32
= 2 × 2 × 3 × 3× 3
= 108
(x) 47089
47089 = 2172
= 217
(xi) 24336
24336 = 22 × 22 × 32 × 132
= 2 × 2 × 3 × 13
= 156
(xii) 190969
190969 = 232 × 192
= 23 × 19
= 437
(xiii) 586756
586756 = 22 × 3832
= 2 × 383
= 766
(xiv) 27225
27225 = 52 × 32 × 112
= 5 × 3 × 11
= 165
(xv) 3013696
3013696 = 26 × 2172
= 23 × 217
= 1736
