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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