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Re: Radicals simplify

  • To: mathgroup at
  • Subject: [mg106372] Re: [mg106361] Radicals simplify
  • From: Murray Eisenberg <murray at>
  • Date: Mon, 11 Jan 2010 05:27:53 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <>
  • Reply-to: murray at

But (x^6 y^3)^(1/4) *is* the correct answer, since from one viewpoint it 
is simpler than the answer x(x^2 y^3)^(1/4) that you prefer.  The issue 
is the simplicity of the structure of the answer.

Evaluate the Depth, or even the TreeForm, of both answers, and you'll 
see that the answer Mathematica gave you is in fact "simpler" in that it 
has a depth of 4, whereas the one you prefer has a depth of 5.

When evaluating a Simplify, by default Mathematica uses a 
ComplexityFunction that counts the subexpressions and digits of 
integers.  (But the documentation seems mute as to exactly how 
Mathematica weighs those two things: just the sum of the two, or what?)

On 1/10/2010 3:30 AM, francix wrote:
> Hi,
> I am using Matematica 7 and need some help with Radicals.
> If I do
> Simplify[(x^4 y^3)^(1/4), x>= 0] I correctly have
> x (y^3)^(1/4)
> But If I do
> Simplify[(x^6 y^3)^(1/4), x>= 0] I get
> (x^6 y^3)^(1/4) and not the correct answer  x(x^2 y^3)^(1/4)
> Thanks in advanced.

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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