Answer: Tree roots can be generally counted on to extend out about one and one half times the diameter of the canopy. So a small tree, with a canopy of maybe 10 feet across will probably have a root system extending out 15' from the trunk. Most tree roots are deep - at least 2-3', but some develop surface roots, as well. In general, a sprinkler system line that is in the top 12" of soil won't be bothered by tree roots. (Deeper lines can be compromised by tree roots.) If the trees you are growing tend to develop surface roots rather than a deep root system, the surface roots can cause problems with the lines. So the answer really depends upon the type of trees you are growing and how deeply you need to place your lines to protect them from winter freezes.
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