One way to get the whole root is to loosen the soil around the root, in a complete circle. Once, in heavy clay, I pulled a big strong root and came up with a solid, conical core of clay clinging to it. It looked like a carrot made of clay!
I can testify: don't let your weeds go to seed! That is a LOSING strategy.
This WW I spike bayonet is my favorite weeding tool. The circular cross section lets me 'swizzle" a circle around the weed. The gradual taper lets me push it deep even in hard clay.
