Hello,
I live in mid-Missouri. I have had this weed on one side of my front lawn since I moved in a couple of years back, and used to just pull them out once every couple of weeks. Finally I got tired, and decided to pull it out with the roots. I dug up around one of the sprouts a bit, and "the roots" are over an inch thick and cross my lawn in several directions. They almost look like they come from a tree, except there's no like tree anywhere nearby. Here are some photos:
Thanks, Paul