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principle root? problem


The other day, I was explaining something to a student regarding solving a
simple algebra problem.  

(x^2-5)^(2/3)=16

The solution to which is easily found. All four that is!  However my version of
Mathematica only gave the two real.  Is there a simple explanation for this?

Also, Mathematica gives the solution to x^(1/2)= -16 as 256. Now, is this a
"principle root" problem and are the two possibly related? Any insights would
be appreciated for this little enigma.

Thanks, 

Rob



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