Square Root Calculation

Date: 01/02/98 at 09:13:37
From: Robert Burdick
Subject: Square root calculation

I can't recall how we used to calculate the square root of a number 
before we learned to push a button on the calculator.

One method, with paper and pencil.

Another method, using calculator for a series of approximations.

Date: 01/02/98 at 18:07:42
From: Doctor Jerry
Subject: Re: square root calculation

Hi Robert,

The following can be used with either paper and pencil or calculator.  

Suppose that you wish to calculate the square root of a number A. The 
divide-and-average algorithm is:

1. Choose a rough approximation G of sqrt(A).  
2. Divide A by G and then average the quotient with G, that is,   
   calculate
                         G* = ((A/G)+G)/2

3. If G* is sufficiently accurate, stop. Otherwise, let G = G* and 
   return to step 2.

Here's an example:  To calculate the sqrt(2), choose G = 1.5.

   G* = (2/1.5 + 1.5)/2 = 1.41666666666
   G* = (2/1.41666666666+1.41666666666)=1.41421568628
   G* = (2/1.41421568628+1.41421568628)=1.41421356238
   G* = (2/1.41421356238+1.41421356238)=1.41421356238

The number of correct decimal places more or less doubles with each 
repetition of step 2.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 01/03/98 at 15:43:21
From: Robert E. Burdick
Subject: square root calculation

Thanks for the solution. It works nicely.