       • To: mathgroup at smc.vnet.net
• Subject: [mg122211] Re: Simplifying radicals
• From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
• Date: Fri, 21 Oct 2011 06:22:27 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j7p1s8\$5ko\$1@smc.vnet.net>

```On Thu, 20 Oct 2011 12:49:28 +0100, Tom De Vries <tidetabletom 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
>

negativeCubeRoot[num_?Negative] := Block[{x},
x /. ToRules@Reduce[num == x^3 && x < 0, x, Reals]
];

negativeCubeRoot[-729]

-9

negativeCubeRoot[-150]

-5^(2/3) 6^(1/3)

negativeCubeRoot[-73.8]

-4.19455

```

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