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Re: Problems with simplify and Sqrt[a^2]

• To: mathgroup at smc.vnet.net
• Subject: [mg73955] Re: Problems with simplify and Sqrt[a^2]
• From: Bill Rowe <readnewsciv at sbcglobal.net>
• Date: Sat, 3 Mar 2007 01:21:01 -0500 (EST)

On 3/2/07 at 6:22 AM, david.shorthouse at credit-suisse.com (dshortho)
wrote:

>any help on this one:

>if you type in: v3/Sqrt[v1^2]/Sqrt[v2^2] - v3/v1/v2

>you get the same expression

>Even if you then type Simplify[%]

>you still get the same expression

>I would have thought Mathematica would have resolved Sqrt[v1^2] to
>v1 (!?)

Mathematica will not do this since Sqrt[v^2]==v is not true for
all possible values of v. In particular for various complex
values. But if you are working with positive reals where this is
true you can get what you want using PowerExpand, i.e.,

In[30]:=
v3/Sqrt[v1^2]/Sqrt[v2^2]-v3/v1/v2//PowerExpand

Out[30]=
0
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