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Re: Possibly related to my post "Unexpected Graph Output"...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125472] Re: Possibly related to my post "Unexpected Graph Output"...
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 15 Mar 2012 00:27:29 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201203140541.AAA25771@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Presumably you're asking about N[(-27)^(1/3)] or (-27.)^(1/3), which 
indeed gives the result you show (i.e., with 6 digits displayed, by 
default). And not asking about (-27)^(1/3).

The reason is that the answer is correct.

To elaborate: by default, Mathematica deals with complex numbers. And in 
particular, the cube-root of a number will be the _principal_ cube root. 
Which is what you've shown (in decimal form).

You'll see that this is a numerical version of -3/2 + ((3*I)/2)*Sqrt[3], 
and that's the root you'll see, e.g., by evaluating:

    ComplexExpand[Solve[z^3 == 27, z]]

Similar questions have been discussed very often in this group.

On 3/14/12 1:41 AM, James Kochanski wrote:
> Why does Mathematica think the cube root of -27 is 1.5 + 2.598076 I and not -3?
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305



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