Okay, so for yesterday afternoon I ended up spraying weed killer around the rocks on the patio and in front of the porch. Since our grandson likes to play in the rocks around the patio, we refuse to use something chemical that could harm him. We use the vinegar, salt and soap solution and it works really well.

Before

About an hour later

That evening

The recipe I use is 1 gallon vinegar, 1/2 cup salt, 2 Tablespoons dish soap. I spray the whole weed and then concentrate on the roots. Make sure you get enough on the plant to saturate it. The best time to spray them is in the early afternoon, after the dew is gone, but with direct sun.