I live out in the country and am plagued with Thistle of all kinds. (along with hundreds of other "weeds")
If I don't catch it real early, I let it get 5" or more, it's ugly, but when you pull it, you get a lot more of the root. I don't think you ever get the entire root, and they grow back, but it's a means of controlling it so it doesn't go to seed. A good deep watering helps with the pulling too.
Not really a solution for a backyard gardener, but I read an article once that said that Thistles regenerates the soil. What is needed when soil lacks fertility is an aggressive plant, one, that grows rapidly and adds organic bulk to the soil and two, deters animals. Let the thistles grow as tall as you then slash them, the thistles lay on the ground as mulch, ready to enrich the soil, not to mention the mass of thistle root material below the surface. This article claimed that areas where the thistle was used as mulch did not have thistle in subsequent years. Apparently, enriched soil is not as likely to grow the beastly stuff.
