My sis has had similar although she broke her bridge. She ended up having an extraction and now has one tooth on a plate. She says it's great.....she is pain free,,,,and more dental treatement free too. This just happened on Wednesday and she is the biggest coward. It's was absolutely fine.
If your dentist can save your tooth then that's what he/she will do.
Hope you remain pain free but given the fact the root is dead you should be fine.
Honeybun
X