A great portion of a tree's roots, about 50% are in the upper 12 to 15 inches of soil under good soil conditions. Very often, however, under clayey soil, 50% of the roots will grow in the top 4 inches and along the surface of lawns, making it difficult to mow, fertilize and aerate the area.
Removing surface roots may harm the tree or make it unstable and prone to falling under windy conditions. Tree roots should not be covered with soil because this may also affect the tree's health.
Try replacing grass near tree roots with other shade-tolerant, ground-cover plants which do not require mowing, or mulch the area to hide the roots while allowing oxygen and water to make their way down to the tree's roots.
For "Mulches" refer to message number 1905.
For more information, see the following Colorado State Extension fact sheet(s).
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Updated Tuesday, June 30, 2015