       Re: Combine sqrts in denominator

• To: mathgroup at smc.vnet.net
• Subject: [mg122438] Re: Combine sqrts in denominator
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 28 Oct 2011 05:37:11 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110271032.GAA08881@smc.vnet.net>

```It only simplifies further if you make certain assumptions, e.g.

Assuming[Element[h | r, Reals], FullSimplify[
1/(Sqrt[Sqrt[h^2 + r^2] - h]*Sqrt[Sqrt[h^2 + r^2] + h])]]

1/Abs[r]

Assuming[Element[h, Reals] && r > 0,
FullSimplify[1/(Sqrt[Sqrt[h^2 + r^2] - h]*Sqrt[Sqrt[h^2 + r^2] + h])]]

1/r

Andrzej Kozlowski

On 27 Oct 2011, at 12:32, Tom D wrote:

> I'm doing a calculation that results in terms of the form
>
> 1/ Sqrt[ -h + Sqrt[h^2 + r^2]] * 1/Sqrt[h + Sqrt[h^2 + r^2]] * (other
> functions)
>
> One sees that this simplifies to (other functions)/r.
>
> It would helpful to make Mathematica perform this simplification, but
> I have not been able to get Simplify[] or FullSimplify[] or anything
> else to do it.
>
> How would I be able to do this?
>
> Thanks,
> Tom
>

```

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