I'm thinking this is Hoary Cress, Cardaria draba aka Lepidum draba.

Here is a link that might be useful: Hoary Cress

Thank you for your response - it sure looks like it and it does not sound like something we should let grow. I guess pulling weeds is on the agenda for tomorrow.

Website I visited says this - does this mean not to pull and must use weed killer? We try not to use chemicals where possible and this stuff is really intertwined with our tulips/lilies/etc

How do I control it?

Mechanical Control

Mechanical removal is strongly discouraged. Small, broken root fragments that are left behind will form a new plant that will produce many more plants.

Herbicide Control

Please refer to the PNW Weed Management Handbook, or contact your county noxious weed coordinator.

This post was edited by HuMan321 on Fri, Apr 18, 14 at 16:30

If it's potentially an invasive weed, you need to take a sample to your Extension Service office to verify the ID.

Locate your county's office with this interactive map
http://www.csrees.usda.gov/Extension/

Here is a link that might be useful: Locate your county's Extension Service office

Many weeds have roots that can keep growing. That's not a reason not to dig it up though. If it keeps growing afterward, you can see where you missed some, so can then get the shovel back out and dig up more roots. Once you get rid of it, keep an eye out for sprouts and it should be a 1-time ordeal. Looks like it's in the process of making a new crop of seeds. I would at least cut it all down for now, to prevent that, if you don't have time to dig it right now.

Mechanical tilling would certainly spread the roots around but hand digging can overcome this kind of perennial weed. I would use a fork rather than a shovel. It will be a slow job: dig up a fork full, shake, remove roots by hand, move along a fork width. Then you will need to keep a close eye out for regrowth and do it all again.

Yes, that's what I meant, not to till, but what you describe sounds way more time and effort-consuming than shoveling up the chunk of soil that comes up with the roots and calling it done, then monitoring for anything that tries to keep growing.

If you have a lot of this material, you can put it in a plastic bag or bin to make sure the roots are all killed, then dump it back into garden. I wouldn't be willing to part with any topsoil over it, or the organic material of the weeds themselves, especially if I've gone to such efforts to harvest it. Weeds contribute by being compostable (as long as they are pulled/dug before they make seeds.)