Between what 2 consecutive integers does / 191 lie

10 and 11

11 and 12

12 and 13

13 and 14

I must assume that you meant "sqrt (191)."

What's the first perfect square greater than 191? Answer: 196 = 14^2

What's the first perfect square smaller than 191? Answer: 169 = 13^2

Note how 169 < 191 < 196. Thus, the square root of 191 lies between 13 and 14.