algebra precalculus - Radical problem: $sqrt[6]{-1}=sqrt{sqrt[3]{-1}}=sqrt {-1}=i$

Thursday 4 April 2019

algebra precalculus - Radical problem: $sqrt[6]{-1}=sqrt{sqrt[3]{-1}}=sqrt {-1}=i$

I'm stuck in a very simple problem . But, I could not find an answer in the books. That's why I want to ask MSE.

Why is not this correct (according to Wolfram Alpha) ?

$\sqrt[6]{-1}=\sqrt{\sqrt[3]{-1}}=\sqrt {-1}=i$

$\sqrt[3]{-1}=-1$, Because, $(-1)^3=-1.$

Where is the mistake?

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