Cut the plant down, cover with plastic, mulch, and wait at least 6 months. I use this method on mulberries and the like very successfully. In my reseeding annual garden I use this method on whole sections when they've gotten too weedy. Just coverage as above and sit some large pots with flowers on top. You still have the garden while all those tough perennial weeds are busy dieing.

Boiling water?

If you can identify the weed, we would have better luck trying to help you. Some difficult weeds like poison ivy die when one cut end is dipped in full strength round up for several days. The PI is pulling the poison directly into the roots, and there's not much impact on the environment. But sometimes you just have to dig to China to get to the roots.

could it be milk thistle? The leaves have stickers on the end. Last year was the first time I saw it around. Dug it out before it got too big.

I've read that there is a Vinegar solution, stronger than the one we use in the kitchen, which kills weeds.

Problem to me is that it would also kill worms and other soil creatures, so I haven't tried it.
Also comes with a warning that it can hurt your eyes, so use with care.

ellen

My wife uses white vinegar on weeds that come through cracks in pavement and bricks. It works very well. I don't think we'd be willing to use it in a large scale way for the reasons outlined by ellenr.

Canada Thistle - is what it appears to be. Multiple lateral growing rhizomes is the problem.

thistle doesn't respond to much, and its seeds have a 90 percent germination rate. if you dig it out when small, you can get the tap root, but once it digs in, it's tough. even a flame weeder won't do more than knock the top growth down temperorarily. go for the roundup (It's not agent orange, by the way, agent orange is paraquat. roundup is glysophate.) at least this product only works on green growing things and is inert once it hits the soil -- unlike caustic vinegar or boiling water, where your soil fauna is the collateral damage.

I agree with elke. I've been using Round up or 3 years and am happy with it. I use it very close to desirable plants with no ill effects. By the way, I consider myself an organic gardener.

I also hate using chemicals and try to pull every weed but you always get some that never leave . How about trying some table salt over it ? It probably will kill it but then nothing will grow for a while . I just tried this around the outside fiberglass containment of my bamboo . Some gets out now and then . I'm trying to keep it out of my neighbors yard . rick

Some weeds are very difficult to kill. Canadian thistle is one of those. My dad has a bad case of canadian thistle, and he dumps a small pile of salt on them. 3 years later he is still battling them. I don't like using chemicals, but I'm recommending to him to use something. Several applications of roundup has got to be better then all the salt he is adding. Strange, adjacent plants don't seem to be affected by the salt.

Vinegar kills the vegetation, but not the roots. It is very effective for the weeds which don't have much of a root system. You also spray only the leaves, and do not drench the soil, so environmental impact is minimal.

I think the only way to get rid bamboo is to dig them. The other alternative offered on the bamboo forum was to nuke them. I have been working on my FILs running bamboo for years. It is no fun.

I think you have burdock. Does it have large leaves? It has the very long taproot that you describe and burrs on a long flowering stem. If it is eat it! The Japanese scrape the root sliver it, fry it in oil and season it with soy sauce, pepper and sugar. Delicious and environmentally sound way to dispose of the weed! Heck if you keep eating it, it won't be a weed anymore.

There isn't much "simple" that is enviromentally (or humanly! with all the problems pesticides cause in humans) "concious" to use. You have to "think big" to manage weeds effectively on a large scale. Plant plants that drown them out (i.e. groundcovers and in flower gardens plants planted wall to wall) or in vegetable gardens hand pulling. One great nitrogen fixing plant I've found as a living weed smothering mulch (some consider it itself weedy but its welcome to me) is white clover (always stays small/low too). :)