You can trim roots, just like you trim the upper part of a plant.
But do not ripped them, crush them or mutilate them; with damage comes rot.
Just cut them with a sharp knife or scissors, and don't try to cut more then a 1/3 of the root mass off. Won't hurt the plant at all, some strains it won't even slow them down some strains will need a couple of days to recover and start growing again.

When your roots grow, you'll see two types, long large roots that tend to grow straight down, these are tap roots and look for water. The smaller hairier roots are the air roots, that fan out closer to the surface looking for oxygen and probably co2 also. (some debate about the roots using co2, some science to support it).

Dutch Masters makes a product called Zone, acts as a bio-fungicide and general healthy root promoter. Works well in recirc systems.