I can't see pictures. Try adding them again or in comments; make sure they turn from greyed to colorful before posting.

Bearded iris would have a rhizome that kind-of looks like a hunk of ginger and fans of broad flat leaves. Siberian iris have fibrous roots and more grassy foliage, sort-of like that of daffodils. There are also iris with bulbs, but I'm less familiar with them.

Another thought, since you said it looked like a small bearded in the photograph, check out woodland iris, such as Iris cristata, it has similar leaves on a smaller scale but the rhizome is smaller and a bit different.

It's not a bearded but there are a lot of species beardless iris that look like that root-wise. I would not immediately assume they are Sibes until I saw them bloom.

I have a few Siberians but their leaves look narrower. They are alive but that's about it. They don't bloom for me; I must have them in the wrong place.

I mostly need to figure out what conditions they like, so I can place them properly.

Sun.

Aside from that, they are pretty tolerant of anything you can throw at them.

They can also take a while to settle in.

Agree with mad_gallica. Even so-called "water" iris will do well in an ordinary garden setting with an ordinary amount of irrigation or rainfall. Sibes - if that's what these are and I am not yet convinced - are dead easy to grow in a mixed perennial border!!

gardengal, which iris are called Water iris? I have pseudacorus I have been trying to grow in a low spot in the yard: that too has never bloomed.

There are many iris that can be considered 'water iris'. The classics among hardy iris are pseudocorus and versicolor. Siberian and Japanese can handle summer water, and I think setosa can also.

Again, I suspect shade with any iris that isn't blooming.

As noted, lots of species of water iris :-) But none require growing in water. A properly watered garden bed is typically sufficient....what most other perennials prefer.

Sun could be an issue for lack of flowering but I find that more of an issue with bearded iris. Most others will tolerate at least partial shade and some even prefer a shady location. I have never found light or partial shade to be much of an issue with Sibes, Japanese iris or pseudacorus and species like I. confusa, japonica, cristata and any of the Pacific coast species or hybrids actually grow better and bloom heavier in less sun and more shade.

Interesting. Make me wonder why my siberians and pseudacorus have never bloomed then. They have not increased either. Whereas other nearby plants are flourishing.

I obtained a japanese iris from someone else and was planning to ask into on that one too.

Since these new ones have roots rather than surface rhizomes I see on my bearded irises, how deep should I plant them? Should I be covering the fleshy horizontal part? Or keeping that on the surface the way I do with bearded irises?

Keep the rhizomes close to the surface, they usually creep along on top.... but don't stress over it, I find them nearly impossible to kill.

I do have one that struggles more than the others and doesn't bloom as much. It probably wanted compost and fertilizer but I ended up just giving it the shovel.