Even if the tree survives the treatment, it is only a temporary solution. Since tree roots grow faster on the top than below, they will soon resurface. So you will still have the problem despite your efforts. Mulches and ground covers are two alternative treatments that can be used to deal with surface roots in the tree border. The tree border is the area between the sidewalk and curb where City trees are planted.
Organic mulches are the best solution.
Mulching also creates a better growing environment for your trees. Best of all, it keeps weed whips and lawn mowers away from the trunk of the tree. When this equipment hits the tree, it damages the trunk - creating entryways for diseases and insects. The larger the mulch area the better for the tree. You may want to mulch just enough area to eliminate the surface root problem.