  Zariski proved the general complex projective curve of genus g>6 is not
rationally uniformized by radicals, that is, admits no map to the projective
line whose Galois group is solvable. We give an example of a genus 7 complex
projective curve Z that is not rationally uniformized by radicals, but such
that there is a finite covering Z' -> Z with Z' rationally uniformized by
radicals. The curve providing the example appears in a paper by Debarre and
Fahlaoui where a construction is given to show the Brill Noether loci W_d(C) in
the Jacobian of a curve C may contain translates of abelian subvarieties not
arising from maps from C to other curves.
