FWIW, central taproots tend to be the exception rather than the norm. And many plants that do have a taproot (or primary stabilizing root) when young outgrow it with age.

From as much as I can see, it looks more weedy than anything else :-)

I'm trying to determine whether the plant in question is Rorippa palustris (usually annual from a taproot), or Rorippa sinuata (perennial from rhizomes).

Based on what is visible in the image the plant doesn't appear to fit either one of those descriptions. It's easier to identify rhizomes in the field since you can dig around the plant to look for them.

As to the plant in question, it had fruits about 0.25 inch long, with petioles roughly the same length, flowers with short yellow petals (maybe a bit over 0.100 inch long), widely scattered stem hairs and a few hairs on abaxial leaf veins, no obvious basal leaf rosette (but was in the water), and cauline leaves that were clasping and auriculate. That fits R. sinuata in the Arkansas key, which is a rare species here. I was planning to use the roots to support that ID, but will have to rely on the other characteristics.

Thanks again.

Regarding the use of roots to id plants. I was wondering whether it is sensible to encourage people to go in that direction, since pulling a plant up will usually kill it. Even if it is transplanted to a garden it might still die or fail to thrive. Are there any laws in the US about uprooting wild plants?

I fully agree with your comments about killing plants. When I find something that isn't known in this area, I sometimes press the plant for submission to our state botanists. However, if it is not plentiful in the area, I take pictures, or a cutting to document it. But when the species is plentiful, or when it is an invasive, weedy species, then I press the entire plant per our Botanists request. According to USDA and other sources, this plant is both weedy and invasive, so I wasn't concerned about pressing it.