Expert: Richard J. Raridon - 7/6/2007

Question
HOW TO SOLVE THE SQUAREROOT OF A NUMBER BY LONG HAND COMPUTATION EXAMPLE:27

Answer
It's sort of like long division.  So you write the number
27.000000 and you work with pairs of digits.  You know that the first number in the answer is 5 so you write
 5.
-------
27.000000
25
----------
 200
next, you double the 5 to get 10. and add a digit to it, estimating how many times that number will go into 200.  
So in this case it's 101 so now you have
   5.1
  _________
  27.000000
  25
___________
101|200
   101
____________
    9900
Then you double the 51 to get 102 and again add a digit to estimate how many times that will go into 9900 so you have 1029
     5.19
   _____________
    27.000000
    25
   ___________
101 | 200
     101
    __________
1029 | 9900
      9261
     _______
       63900
and keep going to get the accuracy you want.  
That's what we had to do back before the days of calculators.