Is there anyway to check the version of an app installed on a iPad without connecting back to iTunes on my desktop / laptop?
iOS provides a list with all installed Apps and their memory usage. Tapping on any App on that list will, besides giving you the option to delete it, display the name, the version, its size and how much memory it's using.
The path to access this list has changed through the iOS versions:
iOS 11: Settings / General / iPad Storage
iOS 9: Settings / General / Storage and iCloud usage / Manage Storage
iOS 8: Settings / General / Usage / Manage Storage
iOS 7: Settings / General / Usage