       Re: (-8)^(1/3) maybe a faq?

• To: mathgroup at smc.vnet.net
• Subject: [mg21040] Re: [mg21016] (-8)^(1/3) maybe a faq?
• From: BobHanlon at aol.com
• Date: Sun, 12 Dec 1999 23:51:08 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```jesse,

There are in general three roots to y^3 = c. For example:

Solve[y^3 == -8, y] // N

{{y -> -2.}, {y -> 1.0000000000000002 + 1.7320508075688772*
I}, {y -> 0.9999999999999993 - 1.7320508075688772*I}}

The default root is complex

(-8)^(1/3) // N

1.0000000000000002 + 1.7320508075688772*I

To force the real root for a plot, make use of the fact: x^3 =
(Sign[x]*Abs[x])^3 = Sign[x]*Abs[x]^3

Plot[Sign[x]*Abs[x]^(1/3), {x, -8, 8}];

Bob Hanlon

In a message dated 12/2/1999 11:05:31 PM, aka007 at mail.com writes:

>maybe this is an faq, i don't know.  i work in a lab
>where calc one students come in and do their work.
>
>the class was doing graphs, or something, involving
>1/3 powers. i don't have the example, this was about a
>month ago.  the teacher was a bit mystified.
>
>what is the deal with this?
>

```

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