The top photo looks like willow herb, Colleen - it's reasonably easy to fork up when it's small like that. If you leave it, it quickly runs to flower and then seeds all over the place. There are several different willow herbs but that doesn't look like the sort with horrible thick roots... however, do an experimental dig underneath it and see! The thick-rooted perennial sorts need very careful digging to remove all the roots - or a weedkiller like glyphosate as it's coming into flower, if you're desperate.
In the second photo there's also a little willow herb - I'd say that one's definitely the easy sort to remove. The more "clumpy" weed looks a bit like shepherd's purse, an annual which is easy to pull out, or hoe when it's small. Not positive, though...
Since 2019 I've lived in east Clare, in the west of Ireland.
I also have loads of this and spent yesterday getting most of it up by hand, because we have had so much rain the borders were still quite damp so it was easy to get out. No doubt I will have missed some and have to do it again and again and again....
Willow herb. One of my "favourite" weeds. Easy to pull, easy to spot, if you miss a couple they grow to knee high overnight so you don't have to bend very far to hoick 'em out, easy to carry because if you have an armful YES! ARMFUL!!! they stick together till you get them to the compost bin.
I have this on damp clay soil next to a dyke at the end of the garden. It's horrible, with very deep roots. I am still digging it out. Dont let it grow and flower as it flings seed everywhere.. Good luck
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In the second photo there's also a little willow herb - I'd say that one's definitely the easy sort to remove. The more "clumpy" weed looks a bit like shepherd's purse, an annual which is easy to pull out, or hoe when it's small. Not positive, though...