  We compute the higher ramification groups and the Artin conductors of radical
extensions of the rationals. As an application, we give formulas for their
discriminant (using the conductor-discriminant formula). The interest in such
number fields is due to the fact that they are among the simplest non-abelian
extensions of the rationals (and so not classified by Class Field Theory). We
show that this extensions have non integer jumps in the superior ramification
groups, contrarily to the case of abelian extensions (as prescribed by
Hasse-Arf theorem).
