Ask Mr. Smarty Plants

You didn't say what tree you have that is breaking the surface with its roots, but it really doesn't matter, there are a number of trees that do that. Most of the roots of trees are within the first 6" to 12" beneath the surface, and extend beyond the dripline (or shadow edge) of the tree. The roots are up there because that is where the bulk of the nutrition, water and oxygen are, and the roots need all three to support the growth of the tree. That pretty much answers your question in terms of adding earth to top the roots. Either the tree will suffer from loss of its essentials, or the root will just grow right back up through the surface, again. Since not much ground cover will grow beneath the shade of a tree, particularly one that has roots on the surface, the best thing to do is mulch the area with a good quality shredded bark mulch. This will have to be replaced from time to time, but as it decomposes, it will add nutrients to the soil, hold in moisture, and protect the roots from heat and cold.This article from Purdue University Extension When Tree Roots Surface gives some more information, and also suggests planting grasses beneath the tree, but our opinion is that is, as you say, a waste of time and money.