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

**References**:**Possibly related to my post "Unexpected Graph Output"...***From:*James Kochanski <jwkochanski@mymail.vcu.edu>