Rationalizing the Denominator

Date: 05/27/97 at 02:25:45
From: r.hassanali
Subject: Algebra

Why do we have to rationalize the denominator?

For example:  1      sqrt(2)
           ------- = ------
           sqrt(2)      2

Date: 06/02/97 at 17:42:35
From: Doctor Mike
Subject: Re: algebra

Hi,
  
Think of it this way.  To do the left one you must do:
                  ____________
       1.4142136 / 1.000000 
    
To do the right one you must do:
            ____________
        2. / 1.4142136    
  
I leave it to you to decide which is more difficult.  Historically,
this is the reason.  The nice thing is that you can get from the left 
to the right by multiplying by "one" in the special form: 

                  sqrt(2)
           1  =  ---------
                  sqrt(2) 
  
Then you simplify.  Pretty neat, eh?  I hope this helps.  

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