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MathGroup Archive 2006

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Re: Forcing surds into the numerator

  • To: mathgroup at
  • Subject: [mg64679] Re: [mg64656] Forcing surds into the numerator
  • From: "David Park" <djmp at>
  • Date: Sun, 26 Feb 2006 05:08:01 -0500 (EST)
  • Sender: owner-wri-mathgroup at


I don't know if there is an automatic method for getting these
simplifications. But they could be done 'by hand'.

step1 = 1/(3 + Sqrt[2]);
Module[{fac = Subtract @@ Denominator[step1]},
  Fold[FullSimplify[#2#1] &, step1, {fac, 1/fac}]
(1/7)*(3 - Sqrt[2])

step2 = Sin[Pi/12];
4# & /@ Apart[step2]/4
(1/4)*(-Sqrt[2] + Sqrt[6])

I'm hoping you will get better answers.

David Park
djmp at

From: Tony King [mailto:mathstutoring at]
To: mathgroup at

Does anyone know how I can force Mathematica to display surds in the
numerator of an expression, or a function that can be applied to do the job?

For example, FullSimplify[1/(3+Sqrt[2])] returns itself and not 1/7

Similarly, Sin[Pi/12] returns (-1+root3)/(2root2) and not 1/4 (root6-root2)

Many thanks


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