Answer: I'm afraid that digging up the roots is the only way you're going to keep them from resprouting in the future. If you leave the root mass in the ground it will send up suckers and then it will begin to decay which will make the soil sink and mushrooms to appear in your lawn. So, prune back the branches and use a chainsaw to cut the trunk down near ground level. Most of the roots will be in the top 12-18" of soil, about 1-2' in all directions from the main trunk.
Good luck with your project!
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