We are going to find the square root of 111.

First, you find the perfect squares that are closest to 111. In this case they would be 10*10=100 and 11*11=121.

Second, you subtract 100 from 121. (121-100=21), divide that by two. (21/2=10.5), and add that to 100 (100+10.5=110.5) to find the number that is exactly between 100 and 121 and its approximate square root (10.5). I checked what 10.5*10.5 is and the answer is 110.25. Since that is so close to 111, I think that the approximate sqaure root of 11 is either going to be 10.5 or 10.6.

Last, we are going to check what 10.6*10.6 is. It equals 112.36.

Since 110.25 is closer to 111, the square root of 111 is 10.6.