Question

Between what 2 consecutive integers does /191 lie

Answer 1

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.