Which of the following is constantly growing in rodents?

hamsters : gotta give them something to gnaw on

LurkingJoker71908, yes, but there are many many other species with claws, the teeth of which, don't grow. It's a singular trait of rodents.

Don't their claws grow too?

I wish I had teeth that could grow and then I could file the cavity part off of the end.

When we used to raise rabbits, we had to keep blocks of wood in their hutches for them to gnaw on.

Sounds like a terrible way for a poor creature to suffer.

As a wildlife rehabilitator, I have had to trim the overgrown incisors of fox squirrels. I can tell you, it's not much fun for either the trimmer or the trimee. But it has to be done.

quicksilver, My oldest daughter had a hamster as a child, loved it and named it "Nubby." As it got older it's sight worsened. One day she was feeding it and accidentally bit her thumb instead of the carrots. The wound became horribly infected. Nubby was our last rodent pet.

claws constantly grow too

kimsharkey625. That's interesting. Something I didn't know