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MathGroup Archive 2000

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Re: Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25265] Re: [mg25258] Question
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 17 Sep 2000 17:33:34 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

on 00.9.17 5:47 PM, Steven Spear at smitsky at mindspring.com wrote:

> Hi, can anyone be so kind as to tell me how this problem:
> 
> 1/cbrt(m) +2    (One over the Cube Root of "m" plus Two)
> 
> ...can be solved in Mathematica by rationalizing the denominator? Thank you.
> Steve
> 
> 
> 
> 

As long as your m is a number the following will work for roots of degree
less than 5:

RationalizeDenominator1[expr_] :=
  
  FullSimplify[expr, ComplexityFunction ->
    (
      Count[#, _?
        (MatchQ[Denominator[#], Power[_, _Rational] _. + _.] &),
        {0, Infinity}
      ] + If[FreeQ[#, Root], 0, 1] &
    )
  ]

For example:

In[3]:=
RationalizeDenominator1[1/(3^(1/3) + 2)]

Out[3]=
1          1/3    2/3
-- (4 - 2 3    + 3   )
11

or

In[4]:=
RationalizeDenominator1[1/(7^(1/4) - 3)]

Out[4]=
1
-- (-27 - 3 Sqrt[7] - Sqrt[2 (63 + 44 Sqrt[7])])
74


It can also be one for expressions involving roots of degree higher than 5
but it is considerably more complicated. In fact already once explained how
to do this in this list (in 1999).
-- 
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/



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