How do I check when I bought an iPad?

I don't believe there's any way to look up the purchase date via serial number as such. If your iPad is still within its warranty period, you can get the approximate purchase date by checking the warranty coverage:

Check Your Service and Support Coverage - Apple Support.

and backdating. If it's out of warranty, though, all it will show is that it's out of coverage. Otherwise, if you don't have your original receipt, you can try contacting whoever you bought the iPad from and ask if they have a record of the purchase.

Regards.