Answer: The answer really depends upon the number of roots in question. A healthy tree should not be bothered too much if you remove some feeder roots as you dig your trench, but might be stressed if you cut away major roots. I'd dig the trench carefully. It should be safe to sever a few roots that are small, but don't sever more than a few. If you find lots of roots 2" or more in diameter where you want to trench, you may want to redesign your project and move it further away from the tree so as not to compromise the tree's health.
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