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This question already has an answer here:

N[(-8)^(1/3)] gives 1. + 1.73205 i.

Since $(-8)^{\frac{1}{3}}$ has three possible solutions, one real and other two are complex.

So, why do not mathematica provides all the three solutions, and if it has to definitely choose only one solution then why not the REAL one ? Just curious !

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marked as duplicate by Daniel Lichtblau, Hector, Sjoerd C. de Vries, Yves Klett, RunnyKine Nov 10 '14 at 8:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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As Bob Hanlon said, you can use CubeRoot to get one root.

According to you question (the tree possible solutions) you can also simply use this:

Solve[x^3 == 8] // N
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