How can I manage surface roots from my scrub oaks?

As the tree roots grow in diameter, they will become a bigger problem. Tree roots will proliferate and thrive where there is water and nutrients so the environment created for the lawn is ideal for tree roots as well. Competition will only increase. Unfortunately, there is no way to eliminate the tree roots without impacting the health of these oaks. Consider developing mulched beds in areas where these large roots are evident (usually close to the stem of the tree). Irrigating heavily and infrequently can encourage deeper root development of the tree but I suspect that the trees have developed many shallow lateral roots that will remain near the surface. Sorry I can’t offer you better options.