A: Why did you come?
B: I just wanted to check out your paintings.
A has mentioned to B that A paints a lot, so B is interested to finally see A's paintings. Is check out natural here to mean "see"? Is it very informal or perfectly natural?
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"Check out" means to intentionally investigate something, to evaluate or otherwise come to a conclusion about it. It does not require seeing, though in this case, you would have to because you can't evaluate paintings by other means. You would check out a restaurant to see whether it was any good before you invited friends there. You would check out a prospective employee to see if he lied on his resume.
Conversely, you can see something without checking it out. A janitor who came to the room to clean up a mess would see any paintings in it, but would not necessarily check them out.