Expert: Richard J. Raridon - 5/4/2007

Question
All right, here is the number you'll teach me with:
                         5
Thank you so much

Answer
write as 5.000000 in order to get the square root to 3 decimals.  You get one decimal in the answer for every two decimals in the original.
So you look at 5 and see that the largest square less than 5 is 4 so the answer is 2.abc
Subtract 4 from 5, leaving 1 and add two zeros to get 100.
Double the 2 in the answer to get 4 and add a to get 4a.
Find the largest value of a such that a times 4a is less than 100.  thus a=2 and you have 2.2bc
2 times 42 = 84 which you subtract from 100 to get 16 and again add two zeros to get 1600.
Again, double the answer to get 44 and add b to get 44b.
Again, find the largest value of b such that b times 44b is less than 1600.  thus b = 3 and you have 2.23c.
3 times 443 = 1329 which you subtract from 1600 to get
271 and add zeros to get 27100.  
Double 223 to 446 and add c to get 446c.  The largest value for c such that c times 446c is less than 27100
gives you c = 6 and your answer is 2.236.  You could keep going if you wanted to get more accuracy.
I know it sounds a bit complicated but, like long division, practice makes perfect.