I have this weed that I cannot get rid of. It is surrounding my sweet
basil, radishes and zucchini. I am hesitant of using a weed killer. If
I knew what it is, I could Google it and get some specific advice.
http://tinyurl.com/nh8b9u

I have that same stuff in my garden..I just pull it up carefully and since
my garden soil is rather "loose", most of the root usually comes with it. No
matter what it is, using a weed killer amongst your veggies probably isnt a
good idea. Depending on how many individual "plants" there are, you "might"
try carefully "painting" them with weed killer to see if it will go down and
kill the root(s).