Square Roots Without a Calculator

Date: 8/6/96 at 17:11:52
From: sjump16
Subject: Square Roots Without a Calculator

How do you get a square root without a calculator? 
What is the square root of 7 to 5 decimal places?

Thanks.
Steve Davis

Date: 8/6/96 at 21:26:54
From: Doctor Robert
Subject: Re: Square Roots Without a Calculator

In order to do this, you have to learn a square root algorithm.  Get 
out a piece of paper and a pencil.  I hope that I can explain it well 
enough just using words. 

First, write down the decimal 7.00000000 and mark off pairs of digits 
starting from the decimal point.  This gives you 7.00'00'00'00'... 

To start, guess at the square root of 7.  The nearest integer(without 
going over) is 2.  Now set the thing up like a long division.  
2 divides into 7 2 times.  2 x 2 = 4.  Subtract that from 7 which 
leaves 3 and bring down the next two digits.  

Now comes the part that's different from division.  The answer showing 
so far is 2.  Double that and use the 4 as the first digit of a new 
divisor.  Whatever goes in the one's place must also go up in the 
answer.  In other words, the question is: forty something goes into 
300 how many times?.  The answer is 6.  Forty-six times six = 276.  
Subtract that from 300 leaving 24.  

Bring down the next two zeros.  Double what's in the answer (double 
26).  Use 52 as the first two digits in a new divisor and the question 
becomes five hundred and twenty something divides into twenty-four 
hundred how many times?  The answer is 4.  4 times 524 = 2096. 

Subtract from 2400.  Bring down two more zeros.  Double the answer and 
leave an empty digit and so on and so forth.  

You can keep going forever.  So now, you know you are smarter than a 
calculator!   

Once you see how this goes, it's not that hard.  If you want a hard 
one, try the algorithm for finding a cube root (I don't know it).  
Hope that you can follow this.
   
-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/