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Calculate the product of two radicals?

POSTED BY: Valeriu Ungureanu
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Use CubeRoot or Surd to get the real-valued roots
POSTED BY: Sander Huisman

Also read:

tutorial/FunctionsThatDoNotHaveUniqueValues

that you can find in the documentation.
POSTED BY: Sander Huisman

Thank you, Sander! It's interesting to observe that Mma has slightly different images for (Power) radicals and (Surd) radicals:

enter image description here
POSTED BY: Valeriu Ungureanu

Branch cuts are not a problem, they are a feature of mathematics.
POSTED BY: Frank Kampas
POSTED BY: Sander Huisman
POSTED BY: Valeriu Ungureanu

The problem appears because of the writing form of the second radical:

enter image description here
POSTED BY: Valeriu Ungureanu

Evidently, it's not a problem to obtain the correct result. But, Mma submit a strange result, especially for some users, e.g. school students.

It's interesting to see the full form of the expression:

enter image description here

In my opinion, the result have to be more rigorous, e.g. to highlight correct result for Reals and Complex numbers, separately.

POSTED BY: Valeriu Ungureanu 
In[5]:= Reduce[Power[x, (3)^-1] Power[x^2, (3)^-1] == x, x, Reals]

Out[5]= x >= 0
POSTED BY: Frank Kampas
POSTED BY: Mariusz Iwaniuk

Unfortunately this can not be simplified without getting into trouble for some numbers:

x^(1/3) ((x^2)^(1/3))
% /. x -> -1.0 - I

or, without complex numbers, just negative numbers:

x^(1/3) ((x^2)^(1/3))
% /. x -> -2.0
POSTED BY: Sander Huisman
POSTED BY: Sander Huisman
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