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

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

or

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

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