Can you be more explicit? What roots are these? I'm having trouble imagining what these roots are as it isn't something I've ever come across. Don't you pull up last years dead plants? Or if some roots are left do they not decompose over the winter? 4 x 8 is tiny and it shouldn't be much work to dig it lightly over. Should take about 10 minutes even if removing last years debris as you go. Could it be that these are roots from surrounding trees rather than last year's veggies?

this will provide more info.
I'm thinking these might be nearby tree roots, as you said.
They're like iron.

Perhaps I should machete the perimeter or a little more and extract them?

Yes, those look like tree roots. They'll always be a problem as the soil in your garden bed is so enticing to them. Since its so small I'd move the bed if possible.

surely wish I could, but that's the best patch of sun. Darn the Luck ! ! !

Been wondering why the return has been so eh the last few years.

thanks floral.

i wonder if I trench with a mattock and line the trench with plastic corrugated roofing, if that would keep the roots at bay for any length of time?

And if so, 1.5lb or 5lb mattock to do the job?