I am in the process of having braces. My lower left premolar has been removed. Today my upper left pre-molar has been removed. However while removing this, my tooth got broke and a small piece has been left in the root itself. My doctor said it is not a problem. He also said if i have to get it removed I will have to go through a minor surgery. So I want to know whether ignoring that can I go ahead with my braces. Will I be able to go for braces keeping that there in the first place. If i have to undergo surgery what are the risks involved? Is it a common problem or a rare risky occurrence?

Thank you for your time and support.