If part of a tooth has already broken from the root, can I get the rest of the tooth pulled or is it surgical?

I have a baby tooth in my mouth since well, I was a baby. Unfortunately there was never an adult tooth to follow and my dentist warned me that the tooth most likely would not last very long. He was obviously right because it had become looser and actually died (I can tell by the discoloration). So my question is, part of the tooth has broke off from the root and in order to get the remainder repaired can they just pull it or would it be surgical? Also how much do you expect it to cost without dental insurance?
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It can be pulled but it may turn out to be a surgical
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