I believe the saying goes: A quintic with rational coeffs is solvable in radicals iff it factors or the Lagrange resolvent sextic (discussed here with JHC decades ago) has a rational root. What about if the quintic has radical coeffs? E.g., the center disk in the D_5 packing if 31 disks has radius a satisfying (43875 + 37180*I) + 74360*(-1)^(1/10) - 97460*(-1)^(3/10) - 70760*(-1)^(2/5) + 70760*(-1)^(3/5) + 23100*(-1)^(7/10) + ((47063255 + 40030096*I) + 80060192*(-1)^(1/10) - 104803824*(-1)^(3/10) - 76142960*(-1)^(2/5) + 76142960*(-1)^(3/5) + 24743632*(-1)^(7/10))*a + ((-4765010 - 4048824*I) - 8097648*(-1)^(1/10) + 10603816*(-1)^(3/10) + 7702560*(-1)^(2/5) - 7702560*(-1)^(3/5) - 2506168*(-1)^(7/10))*a^2 + ((1630 + 336*I) + 672*(-1)^(1/10) - 1584*(-1)^(3/10) - 1040*(-1)^(2/5) + 1040*(-1)^(3/5) + 912*(-1)^(7/10))*a^3 + ((-225 + 1116*I) + 2232*(-1)^(1/10) - 2964*(-1)^(3/10) + 200*(-1)^(2/5) - 200*(-1)^(3/5) + 732*(-1)^(7/10))*a^4 - 5*a^5 Can we say that such a quintic is solvable in radicals iff the resolvent has a root expressible in radicals? If not can we at least say that no resolvent solution implies no quintic solution? -rwg I have the resolventin Mma (LeafCount 3029) and Macsyma, if anyone wants. OLEO-GUM-RESIN NUMEROLOGIES