# Is an nth root of unity a square?

Suppose w^(2n)=1 (w is a complex number). For which n (if any) \sqrt(w) \in Q(w) ?

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is it homework ? –  David Lehavi Oct 22 '09 at 7:38
Perhaps the title should say something about the field Q(w)... how about "Is root of unity w a square in Q(w)?" –  Ilya Nikokoshev Oct 22 '09 at 8:01
This could be homework for a second course in number theory, but it also could be a lemma needed by someone in a field far from number theory. I would leave this open. –  David Speyer Oct 22 '09 at 10:44