Problem calculating an expression with roots

[retoa]

(02-03-2015 11:59 AM)Snorre Wrote:  If you enter it as ³√(-8) you'll get -2.
(The other way around is similiar: (1/3)NTHROOT(-2) is not the same as (-2)^3)

That with \( \sqrt[3](-8) \) the answer is -2 is quite clear.

I tried \( \sqrt[1/3](-2) \) in both home and CAS

in CAS the answer is -8
in home (complex) it is -8.00000000002-7.58171027068E-11*i, so the imaginary part is almost zero.
As the imaginary part is not exactly zero the answer is not real and can not be displayed in real mode. I don't know if the Prime tries to calculate it and comes to a non real answer or it avoid calculating it, the error is "Error: (X<0)^(not in Z)". Actually the exponent is 3 and is in Z.
I know it does not make much sense to use \( \sqrt[1/3](-2) \) instead of (-2)^3, but it is interesting to see that in home it comes to a complex approximation of a real number (natural number actually).

Regards

reto