Root left behind after extraction?

Because the top of the tooth was weak and brittle the dentist didnt pull the tooth out she split it in half using the drill and removed 1/2 roots but left the rest behind. WHen i poke it with my tongue i dont feel any hole but a lot of tooth as if a lot was left behind. The dentist told me that this is fine and that it'll push its way out? Is this true because it isnt small bony splinters its a large root? Thanks