Under Root
 

     Now learn a very easy method -how to find  under root of any number
                     Let  see this example; Find the under root of 39

Here  we know that perfect square near to 39 is 36 and under root of 36 is 6
So under root of 39 is more than 6  Let we take under root of 39 is 6.2 by approximation
Divide 39 by 6.2

                39   =  6.290
         6.2          
Now take average of 6.290 and 6.2   and again divide 39 by this average
(6.290+6.3)/2= 6.295
                       39   =      6.195 
             6.295            

Now this 6.195 is near to under root of 39  again we take average  of this number with last 6.290
6.290+6.195/ 2    =6.242    divide  39 by this 6.242

                     39       =6.247
   6.242

 This  6.247 is very very near to our required answer
If we  again repeat this step one more time our answer is more accurate

 See one more example  : Find the under root of  89

              89 = 9.46
   9.4  

   Here we take 9.4 by approximation considering  9 is under root of 81 

                    89         =9.43
9.43

9.43 is average of 9.46 and 9.4 .       9.43 is under root of 89 up to two places of decimal