square root long division method: root 24 trouble I'm trying to get a grasp of the long division method of square roots without a calculator via pen and paper, but i'm having some trouble. I've been trying to increase understanding with practice, and decided the square root of 24 was a good number, since its so close to 25, i know what to expect.
Well, everything seemed to go ok until i got to 4.89 then started to break down. i double checked my work and found i'd screwed up on my multiplication, and restarted, and got to 4.89897, but then something breaks down because my pen and paper says the next number is 8, but my calculator says the next number is 9.
I don't understand why my progress would get so close to exact and then suddenly flip out and produce the wrong number.

My hope is that i messed up somewhere stupid like subtraction or multiplication. Otherwise i think im doing it completely wrong and getting the first 6 digits right is a crazy coincidence.

I recommend to check $9788 \times 8$ again. 
