Re: Cube root of -1 and 1

*To*: mathgroup at smc.vnet.net*Subject*: [mg90881] Re: Cube root of -1 and 1*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Mon, 28 Jul 2008 07:51:30 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <g6h5fm$h26$1@smc.vnet.net>

Bob F wrote: > Could someone explain why Mathematica evaluates these so differently? > > In[53]:= > > (Sqrt[36] - 7)^(1/3) > (Sqrt[36] - 5)^(1/3) > > Out[53]= (-1)^(1/3) > > Out[54]= 1 > > In other words why isn't (-1)^1/3 expressed as -1 ?? Branch cut and principal root are the key words here. See, "How do I get x^(1/3) (where x is a negative number) to evaluate to a real number?" http://support.wolfram.com/mathematica/mathematics/algebra/realpower.html Regards, -- Jean-Marc