SIMPLIFY AND SQUARE ROOTS

• To: mathgroup at smc.vnet.net
• Subject: [mg18294] SIMPLIFY AND SQUARE ROOTS
• From: Blimbaum Jerry DLPC <BlimbaumJE at ncsc.navy.mil>
• Date: Fri, 25 Jun 1999 15:05:34 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```n article <7kpage\$49n at smc.vnet.net>,
"efarr" <efarr at farr-research.com> wrote:
> Hello,
>
> Try typing in the following in a new session of Mathematica (I'm currently
> running ver 3.0 under WinNT).
>
> Simplify[ Sqrt[b^2]*Sqrt[1/b^2] ]
>
> It seems like the b's should cancel, and I should get 1. Why don't I? Is
> there any workaround?
>
In a previous reply I commented that even FullSimplify wouldnt get
you the result that you wanted but PowerExpand (it assumes all the variables
are real) would.  But theres more to it.  After reading the manual (shame on
me for not reading it the first time), I quote from Mathematica v3. p. 95:

"The basic operations of Mathematica are nevertheless carefully set
up so that whenever possible the results obtained will be valid for almost
all values of each variable."

Then an example is given that Sqrt[x^2} is not automatically
replaced by x and the reason, which makes sense, is given why this is not
done.

Hence, when you use Simplify or FullSimplify I assume that this Mathematica
rule kicks in and you dont get the result you wanted or expected.  This

example shows why this rule, although it makes perfect sense for the example
Sqrt[x^2] doesnt make sense for the example

Simplify[Sqrt[b^2]*Sqrt[1/b^2].

Note also that you arent necessarily stuck with what Mathematica
does.  For example, you could have written your own transformation rule to
get what you want:

Sqrt[b^2]*Sqrt[1/b^2]/.{Sqrt[(x_^2)]->x,Sqrt[(1/x_^2)]->1/x}

You probably wouldnt want to do this but I'm just showing it to you
to see that there are other options.

Jerry Blimbaum   NSWC   Panama City, Fl

```

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