My
experience is that the more you pull or dig the ground, the more vigorous the nettles grow back. If you have most definitely decided that you don't want the nettles there, the best way I've found is change the nature of the soil. Nettles love moist, highly fertile, and acid soil. Usually adding a lot of lime or
wood ash will reduce the nettle population pretty quickly, but may need reapplying every year or few. Physically changing the drainage also does it quickly. Growing something like willows will change the drainage in a few years, and compete with the nettles for
water.
That said, you would be amazed how useful a nettle patch can be. Nettles make food, medicine, clothing, natural plant fertilizer, natural pesticides, rennet substitute, a substitute for some or all of the curing salts when curing meat, natural clothing dye, and a very handsome
profit as U-pick nettles. I also sell/trade mine with the goat lady and she uses it for a nutritional supplement for sheep and goats. They are also useful for teaching kids to listen to you when you tell them not to touch this plant because it hurts, they touch the plant, they realized you might be on to something and worth listening to in the future... or at least, that's how I remember it from my childhood. Nettles almost always grow with a companion plant that neutralizes the sting. Here it's dock weed, other places, other plants.