Making a complete idiot out of yourself just for the purpose of appearing approachable is disingenuous at its core. All it will achieve is making you appear as if you are not fully qualified for the position, and create unnecessary doubt in others regarding your ability to contribute positively and adequately respond to their needs.
You can make yourself approachable without having to make yourself look like someone you're not. You want people to view you as intelligent, reliable, and helpful. Listen more than you talk. Answer the questions you're asked honestly, completely, and descriptively. Ask people for feedback when you help them and when they help you. Be genuinely interested in who they are as a person, not just as a coworker. You don't have to be best friends, but you also don't want to create artificial boundaries, either.
It's really not that hard if you take the time and effort to understand that even though it's work, there is a social perspective which cannot be ignored.