I have a tooth broken off at gum my dentist says I need oral surgury to take it out, can I avoid this? Won't my gums grow over it an seal it, its almost below the gum . Just a tiny micrometer is left above the gum.

No they won't. Listen to your dentist.

If the root is not removed you are only asking for trouble, bacteria has direct access to your nerves and blood vessels, these will quickly become infected and you will end up getting the root removed anyway + having to probably sit through the pain of having an oral infection..

I must ask... this is the third post (that I have seen) asking about somewhat different things, are these questions about completely different teeth?