I am very curious to know about the roots Cookies4kids and Pandora are having problems with. I plant my hostas under oaks and near oaks. I don't seem to have much problem (so far) with what I would consider major roots. But, I have always had problems in the beds with a mesh of very fine roots. When I dig in those beds the entire area is full of the very fine roots and I have to pull them out and shake all the soil off of them. I just went out and dug a hole about one foot square and this pile of fine roots is what come out of that small area. I have always assumed they were Oak roots but can not trace them to anything, they are pretty easy to pull out and come out in large clumps.
Small shallow hole:
Roots out of that small shallow hole: