I bought a package of 3 pastel dahlias on a sales table: I expected that most had dried out and were goners, but I discovered what I had were 3 divisions - each with about 6-8 tubers (most with one root) dangling(still attached) underneath.

I added several handfuls of moist potting soil, covering the divisions/tubers/roots completely until I could ask:

Do I cut the tubers free of their division stem and plant them???
OR
Do I plant each division with all its attached tubers???

I am slowly transforming (over 3 years) a full sun compost-filled and yearly amended with organic matter raised bed into a perennial flower bed with low/no maintenance plants that strike my eye.

But I don't know anything about dahlias other than their picture looked pretty.
(Especially if I must dig up the bulbs every fall and re-plant them the next spring??)

Your description of the tubers/roots is hard for me to follow.
How about you post a photo?

As it's after midnight here, I'll first try to clarify with words; pictures will have to wait until I sleep about 8 hours or so. After my coffee, I will unearth the plant material and take pictures for you to visualize what I tried to describe.

The bag I bought said 3 [different] pastels of dahlias; there were 3 separate masses, each one starting with part of a stalk that seemed to be the result of the division of a much larger plant (sso I called each mass a division). Underneath each division/mass are long roots? of various lengths with enlarged sections (that I called tubers), most of which had one root coming out the bottom (or where the original root that started BEFORE it became enlarged then continued).

Any dangling tubers will not be viable. A portion of the crown is required for growth. The mass with the crown and attached tubers is what you want to plant.

100% true, Gary! I've been told you can leave those danglers on the clump when you plant. But I'm always afraid those will rot and maybe spread rot to the rest of the clump. So I trim them off.

Thanks, Dan! I was wondering if I should just cut those danglers off now, while I'm letting the clumps dry. . .

I would leave them if they aren't broken, otherwise remove the ones that are.