Check it out?

If you see this in a bookstore, take it to the checkout.
If you see this at the library, check it out!
Where did that expression come from?
Surely not the library! It must be from retail...
Check out means to pay one's bill and depart, as from a hotel or restaurant. It does not specifically refer to the library procedure of checking out a book. But that's just me, I frequent libraries more than hotels or motels. No one else would notice such an omission.
Check-out means the counter where you pay at a supermarket or other store.

There are many expressions that employ the word "check," but check it out is not in my dictionary. I'll do some further checking...

Please keep your impatience in check while I check up on this...

Let me check in with another reference book...

Check it out is not in any of my reference books, so it must be a young expression, not an old saying.