Is there a large tree or some large shrubs nearby? These roots might be coming off something like that, especially trees...

One of those roots also looks like grass rhizomes. Is there a lot of grass coming up among your veggies, Jim?

hello and welcome to GoY.

they are certainly roots of some kind. and as suggested they do look like the fibrous roots of a tree or shrub. These may be in a neighbours garden so not your plants but roots extend a substantial distance. [had they been very fine, hair like, I'd have gone for fungal growth which is totally harmless and needed for healthy soil and plant growth.]

if they belong to an actively growing tree they will compete with your veg for water and nutrients but they wont necessarily do them any harm. they would grow slower and be smaller so you'd get less crop.

You will have to add more manure/fertilizer and water to get the veg to grow well.

hope this helps.

Do you mean your soil is hard? Try this test: put a large spoonful into a glass jar of water and leave it to settle for a while.It may all settle heavily to the bottom of the jar and leave the water fairly clear. Or you might find various bits floating on top. You may get some settling to the bottom but leaving the water dirty.If nothing floats you need to add humus - which means add some compost, well rotted dead leaves etc to your soil. If what falls to the bottom is smooth and rather slippery between your fingers it is clay and you will need to add some coarse grit as well as the compost.

If you have a lawn try leaving your lawn mowings on your veg plot over the winter and then dig them in when Spring arrives. Then you can add some general fertilizer. I have seen advice not to do this but I found it worked extremely well on some very poor soil I had. Of course home made compost is better but we don't all have enough of it!

Can you lift the root things off or are they attached to something under the soil?

Thank you for all your kindness answers and help me find out my garden problems .
My vegetable garden bed , I did put Liner pond On top concrete before put the garden soil, not thing touched into ground soil .no grass around my vegetable garden bed.
any time before I m planting My vegetable, I did pull all of those “brown roots , white roots “out , put some kind of “ weedS killer “, but the kind of that problems Still come back the same way.
I see all of “ white roots “ grow from the soil and the end of season it seam more mature, it turns brown and strong It hard to break it by hand. 😩
Thank you all for your help answers
Sincerely.

Well, they still sound like some kind of tree or shrub roots. I've often been amazed the way that roots will travel through the tiniest cracks in concrete, and the smallest pinholes in pond liners, in search of water and good soil. the only weed killer that would be effective in stopping them would not be safe to use with veggies, and copper screening, while safe and effective, is pretty expensive. I would carefully empty the bed, and find out where those roots are coming from. You can then decide to either seal the openings, or rebuild the bed somewhere else. Note that I wouldn't line a veggie bed with pond liner: it would keep the soil way too wet, even if it was perforated.