The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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,   
                         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!   

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

Thanks for the solution. It works nicely.
Associated Topics:
Middle School Square Roots

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.