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If in WolframAlpha I put `(-8)^(2/3)`

then it outputs the main root and 3 roots solution too (to the end in a polar graphic).
How can I get the 3 root solution of `(-8)^(2/3)`

in Mathematica Desktop?

I tried with: `Solve[(x^(3/2) + 8 == 0), VerifySolutions -> False]`

but the output is `{{x -> -2 + 2 I Sqrt[3]}}`

... I don't understand, help me please.

`NSolve[x^(3/2) + 8 == 0, x]`

gives two solutions`{{x -> -2. + 3.4641 I}, {x -> -2. - 3.4641 I}}`

– Ulrich Neumann – 2018-09-20T15:17:43.087thanks for you request, but the real root is not here, I'd like in algebraic form too. – Javier Giménez Moya – 2018-09-20T15:19:46.317

1Maybe `In[921]:= Solve[x^3 == (-8)^2, x]

Out[921]= {{x -> 4}, {x -> -4 (-1)^(1/3)}, {x -> 4 (-1)^(2/3)}}` ?? – Daniel Lichtblau – 2018-09-20T15:22:31.800

@ Javier Giménez Moya Ok, but the number of solutions might find your attention – Ulrich Neumann – 2018-09-20T15:23:01.077

2The real "root" is not a valid solution of

`x^(3/2) + 8 == 0`

, so the WolframAlpha polar plot output is misleading at best. – Carl Woll – 2018-09-20T15:24:21.727I thougth that if Power[(-8)^2, (3)^-1] was 4, then almost one root for (-8)^(2/3) was 4 too. – Javier Giménez Moya – 2018-09-20T15:39:41.103