2 Divided by the Square Root of 2

Date: 11/10/95 at 7:58:7
From: Braun Tillmann
Subject: math

Why does 2/sqrt 2=sqrt 2 ?

Date: 11/10/95 at 11:10:41
From: Doctor Ken
Subject: Re: math

Hello there!

I think that the easiest way to see this problem is to realize that
2 = Sqrt{2} * Sqrt{2}.  So the left part of your equation becomes

  Sqrt{2} * Sqrt{2}
  ----------------- 
       Sqrt{2}

and you can see that that equals Sqrt{2} by cancellation.


Actually, it will work for any number, not just 2 (as long as the number is
bigger than zero).  Let's say you have a positive number, and let's call it
x.  Then we can just replace the 2 by an x and everything still works:

                                x         Sqrt{x} * Sqrt{x}
x = Sqrt{x} * Sqrt{x}.   So  -------  =   ----------------- 
                             Sqrt{x}          Sqrt{x}       ,


and you can see that that equals Sqrt{x} by cancellation.

In fact, if you know about imaginary numbers, then the above proof works for
ANY x, as long as it's not zero.

-Doctor Ken,  The Geometry Forum