Answer: Weed identification can be very difficult, particularly when it's not flowering. It's also hard to identify weeds based on short descriptions, and the fact that weeds vary greatly by region makes it even more complicated.
Your best bet in identifying your weeds may be taking a look at the surrounding environment. One of your neighbors may be cultivating the plant that's sending roots into your yard.
If you don't see anything around that might have caused the problem, try doing an online search or visiting a library for a book that shows pictures of common weeds. It may be easiest to identify what you have by comparing photos. Once you've identified the weeds, you're well on the road to treating them.
I think I'd be curious enough to dig the around the root and follow it to its point of origin.
Wish I had more to offer!
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