bunch of roots that go out in all directions. Pruning one root shouldn't cause any harm to the tree, and it is probably just one root that is the problem. It might take some digging to find where exactly the root is crossing the sidewalk, but once you locate it, completely severing it should be enough to stop the sidewalk from raising any further (for a while--eventually the tree will probably grow another root in that direction, but that should take a good long while).