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MathGroup Archive 1996

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Re: Simplifying Expressions containing SQRT

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3162] Re: [mg3126] Simplifying Expressions containing SQRT
  • From: jpk at apex.mpe.FTA-Berlin.de (Jens-Peer Kuska)
  • Date: Fri, 9 Feb 1996 03:02:17 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

> Hi everybody!
> 
> Strange things do happen!
> 
> Mathematica4s ability to simplify equitations containing square roots
> seems to be quite weak. Perhaps I just do not know enough about these
> things, but I did read the manual. An example:
> 
>              Sqrt [ R ( R - x ) ] Sqrt [ ( R - x ) x ] / ( R x - R^2 )
> 
> 
> equals Sqrt[ R / x ], but I can4t get Mathematica figure that out.
> 
> I tried PowerExpand, Factor, Collect, Simplify and almost everything
> else in various orders. Nothing worked! What can I do?
> 
> I do appreciate every helpful hint. Thank you very much.
> 
> 
> Eric von Lieres                         lieres at studm.hrz.uni-siegen.de
> 
> ------------------------------------------------------------
Hi Eric,

Try

In[]:= test=Sqrt[R*(R-x)]*Sqrt[(R-x)*x]/(R*x-R^2)

Out[]=
Sqrt[R (R - x)] Sqrt[(R - x) x]
-------------------------------
             2
           -R  + R x


In[]:= test //. {
             Sqrt[a_]*Sqrt[b_] :>
               Sqrt[a*b],
             Sqrt[a_]/b_ :> 
               Sqrt[Simplify[a/b^2]]
               }  

Out[]=
     x
Sqrt[-]
     R

You see, it is not obvious that yields a simplification in general, but
here it works fine.

Hope that helps
Jens



> Eric von Lieres               lieres at studm.hrz.uni-siegen.de
> 
> 
> 


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