• To: mathgroup at smc.vnet.net
• Subject: [mg122219] Re: Simplifying radicals
• From: dimitris <dimmechan at yahoo.com>
• Date: Fri, 21 Oct 2011 06:23:54 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j7p1s8\$5ko\$1@smc.vnet.net>

```On Oct 20, 2:49 pm, Tom De Vries <tidetable... at gmail.com> wrote:
> Hi,  I'm working with some introductory topics in radicals.
>
> I know that Mathematica assumes things about the domain used in
> problems,  so the principal cube root of a negative number will be
> complex... or something like that..
>
> I'm way down at the lower high school level simply working with cube
> roots of negative numbers and wanting a negative number result.
>
> I know there are ways of using assumptions and solving over the reals, etc.
>
> Is there any EASY way I can simply ask for the cube root of -729 and get -9?
>
> TOM

Hello.

In[1]:=mycuberoot[x_] := Block[{w}, w = w /. Solve[w^3 == 1][[3]]=
;
If[Re[x] < 0, w*x^(1/3), x^(1/3)]]

In[2]:= mycuberoot[-729]
Out[2]= -9

In[17]:= {2 - Sqrt[5], 2 + Sqrt[5]}^(1/3)
N[%]

Out[17]= {(2 - Sqrt[5])^(1/3), (2 + Sqrt[5])^(1/3)}  (*Mathematica by
her defaults evaluates (2 - Sqrt[5])^(1/3) to be a complex number*)
Out[18]= {0.30901699437494756 + 0.535233134659635*I,
1.618033988749895}

In[19]:= mycuberoot /@ {2 - Sqrt[5], 2 + Sqrt[5]}
Chop[N[%]]

Out[19]= {(-1)^(2/3)*(2 - Sqrt[5])^(1/3), (2 + Sqrt[5])^(1/3)}
Out[20]= {-0.618033988749895, 1.618033988749895}

For versions up to 5.2 you can also load the package RealOnly.

In[1]:=Needs["Miscellaneous`RealOnly`"]

In[2]:=
(-729)^(1/3)

Out[2]=
-9

Keep in mind that perhaps will be some conflicts with built in
functions like Simplify.