Your weed sounds very much like Ground Elder (syn. Bishops Weed). The
botanical name is Aegopodium podagaria.
Have another look at your weed: does it have a compound leaf made up of 5
leaflets? Ground Elder definitely has endless white roots and a rapid rate
of spread. It is an umbellifer with a white summer flower.
RoundUp should certainly help, as would any herbicide with Glyphosate in it.
Digging up the root very thoroughly will slow it down, making herbicide
application easier and less expensive. However, if it is coming in from a
neighbour's garden, you may have to learn to live with some of it!
SPIDER

Mike1 wrote in message
...
I have a similar problem with diagnosing a weed that has appeared in my
garden this Summer, but not that I can recall in previous years.

It has green jagged leaves and appears very quickly. In a small patch I
have seen five different clumps of these leaves.

If I dig one up, I see a single thin white root which I can never get to
the
end of. This stuff has already started to appear in other parts of the
garden about 30ft away.

Recently I have started to use Roundup on the leaves and hope this will
eventually get down to the roots and source.

Any ideas whether it is bindweed or some other super weed ?

Mike.