       • To: mathgroup at smc.vnet.net
• Subject: [mg122208] Re: Simplifying radicals
• From: Syd Geraghty <sydgeraghty at me.com>
• Date: Fri, 21 Oct 2011 06:21:55 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110201144.HAA05716@smc.vnet.net>

```Hi Tom,

Piqued by your question I decided to respond in a way that has been little used by the regular respondents to MathGroup.

I used the following free form inputs (type == at the start of a Mathematica 8 input followed by the english language question). This approach gets Wolfram|Alpha results that initially point to a basic contradiction in Mathematica 8/Wolfram|Alpha.

So:

== is the cube root of -729 equal to -9

which yields Input Subpod content:

"(-729)^(1/3) = -9"

With the Result Subpod output:

False

As opposed to

== is the cube of -9 equal to -729

which yields Input Subpod content:

"(-9)^3 = -729"

With the Result Subpod output:

True

So evidently Wolfram|Alpha fails to meet your reasonable question:

"Is there any EASY way I can simply ask for the cube root of -729 and get -9?"

The root cause (pardon the pun) of Mathematica's stubborn refusal to cooperate with your quest is illustrated by:

== real value of cube root of -1

which yields Input Subpod content:

WolframAlpha["real value of cube root of -1", {{"Input", 1},  "Plaintext"}]

With the Result Subpod output:

"(-1)^(1/3) is not a real number"

The pure function InputForm

(N[#1, 1] \[Element] Reals &)[(-1)^(1/3)]

giving:

False

illustrates the reason that Mathematica stubbornly opposes giving you the solution you want.

I hope someone from the Wolfram|Alpha community at WRI gets interested in and responds to the issues inherently associated with getting sensible answers to classes of questions involving inverse functions when input in free form to Mathematica.

Cheers .... Syd

Syd Geraghty B.Sc, M.Sc.

sydgeraghty at me.com

Mathematica 8.0 for Mac OS X x86 (64-bit) (February 23, 2011)
ReleaseID:    8.0.1.0 (2063982, 2063639)
MacOS X V 10.7.1 Lion
MacBook Pro 2.33 GHz Intel Core 2 Duo  3GB RAM

On Oct 20, 2011, at 4:44 AM, Tom De Vries 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
>

```

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