Dentist cracked my Wisdom Tooth during Extraction?

I went in on Tuesday to get my lower wisdom tooth extracted, and my dentist had a really tough time getting it out. He was twisting and pulling the best I can recollect.....then Crack!!!!! When he finally did get it out, he pointed out that one of the prongs or roots had snapped off from the tooth itself...presumably from the crack noise we all heard. My dentists said that the roots doesn't get infected and that after the extraction site heals, everything will be fine. I don't know but it kind of worries me. Has anyone experienced this or am I the only one? What are the possible effects of this? I'm not buying what my dentist is telling me.