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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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