Here's a good discussion of roots:
"There are many misconceptions about root growth in trees. Horizontal root spread is one of the more important. It is often said that the majority of feeder roots are concentrated at the dripline of the tree. Roots extend to that distance and much farther. Studies have shown root spread to be 4 to 7 times the dripline distance (radius) of the tree
. This is an important fact to remember when applying herbicides, fertilizers, insecticides, and other soil treatments around trees. Careful consideration can prevent serious injury to your trees."