Tree root systems do not grow very deep. Tree's roots grow shallow and wide. Do not cut them! Tap root? Okay, many conifers have tap roots extending deep into the soil, however they still rely on surface roots for oxygen, moisture, and nutrients. In general, tree roots are close to the surface, extend laterally from the tree (like spokes on a bicycle wheel), and extend far beyond the canopy of the tree. Commonly, roots will extend well beyond 2 to 3 times outside of the drip-line. Roots have been found more than 10 times beyond the distance from the trunk to the canopy.
The general consensus is that roots tend to be double the tree's height and about as least twenty feet in each direction depending on how old the tree is. It depends on the type of tree and the conditions in which it is growing. Trees are like people they are basically lazy so they will only put roots out as far as they have to to supply nutrients and support.
Tree roots grow where there is an abundance of oxygen, water, and nutreints. Which is where? Where the soil meets the air.