Mr.Oldfield is teaching us how to approximate square roots. We are using perfect squares to estimate what a imperfect square would be. A perfect square is a number that can be squared and there is no decimal. For example, 36, 100, and 64 are all perfect squares because 6*6=36, 10*10=100, and 8*8=64. Examples of imperfect squares would be  17, 46, and 90. These are imperfect squares because the number that has to be squared to get them is a decimal.

My number that I had to find the square root for is 111. This is not a perfect square which makes it more difficult to do. i know that 111 is in between 100 and 121, which are both perfect squares. The square root of 100 is 10 and the square root of 121 is 11. This means that the square root of 111 is in between 10 and 11.

The first step that I take is to find the exact middle of 100 and 121, which is 110.25. I found this number by squaring 10.5. I know that 111 is bigger than this number, but not by much. the next thing I did is squared 10.6 to get 112.36, which is a little bigger than 111. I now know that the square root of 111 is in between 10.5 and 10.6. This alone narrows it down quite a bit, but you could go to the hundredths place if you want to.

To narrow it down more you would just keep applying the steps you have used so far to keep trying to find the exact square root. I personally just go to the tenths place and stop there. I know that the answer is in between 10.5 and 10.6 which is in between two decimals.