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Re: Simplfying inside Sqrt

  • To: mathgroup at
  • Subject: [mg55127] Re: [mg55106] Simplfying inside Sqrt
  • From: "David Park" <djmp at>
  • Date: Sun, 13 Mar 2005 04:57:46 -0500 (EST)
  • Sender: owner-wri-mathgroup at


How about...

{Sqrt[x^2 + x^4], 1/Sqrt[x^2 + x^4]};
% /. Power[a_, q : (1/2) | (-1/2)] :> Power[Factor[a], q]
Refine[%, x > 0]
{Sqrt[x^2*(1 + x^2)], 1/Sqrt[x^2*(1 + x^2)]}
{x*Sqrt[1 + x^2], 1/(x*Sqrt[1 + x^2])}

David Park
djmp at 

From: billkavanagh at [mailto:billkavanagh at]
To: mathgroup at


I'm wondering how to tell mathematica that I want terms like
Sqrt[x^2+x^4] to be x*Sqrt[1+x^2].   I have an expression with a few
terms like this in it so manually inserting a
PowerExpand[Sqrt[Expand[x^2+x^4]] is no good to me.

I've tried a general PowerExpand and Simplify with a Im[x]==0 around
the whole expression but with no luck.

Does anybody know how to do this?


William R. Kavanagh

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