find the nearest numbers that are greater and less that your number, in this case, 7 and 8 which square to 49 and 64 and average them by adding them together and dividing by two. 7+8=15 15/2=7.5 7.5 is the nearest estimated square root of 50 that I can get, but the real answer is about 7.071067811865475. (I used a calculator)
