# number theory – Galois elements determined by an action on the roots of the rationals?

Can there be an element $$sigma$$ of $$Gal ( overline { mathbb {Q}} / mathbb {Q})$$, other than identity and complex conjugation, which is completely determined up to conjugation by its action on $$sqrt[n]r$$ for everyone $$r in mathbb {Q}$$ and all $$n in mathbb {N}$$?

I'm expecting no, but if I'm wrong, can the subgroup of such elements be given another characterization?