Place a lawn decoration or piece of lawn furniture directly over the root to deter traffic from the root. For example, insert a hand-carved sign with your family name on it beside the root. This will prevent children and adults from walking directly over the location of the root, preventing accidents. This will only work if the exposed root is not very large and if the location of the root seems appropriate for just such a decoration.
Cover the root with a light layer of mulch. Mulch will not prevent oxygen from reaching the root, but may cover the most dangerous part of the root. The mulch should be no more than 2 inches thick. You may need to replenish the mulch once or twice a year.
Plant a ground cover over the root. This will cover the root and also prevent anyone from walking in the area. Ground covers are vining and creeping plants that cover an extensive area in a short amount of time. Many types of ground cover will grow with minimal care. Till the ground around the tree root, then lay a little peat moss in the area. Do not cover the tree root at any point during this process. Place seeds in the soil according to the instructions, then water. You will need to water your ground cover frequently in the first year of its growth.