What is a word that contains the root word ite?
There is no root "ite."
There is a root "iter, itineris" meaning a road or pathway:
Itinerary, itinerant.
There is the root "iter" meaning again: iterate, iteration.
There is the suffix "-ite" meaning an inhabitant or an adherant;
also "-ite" meaning a salt or acid whose adjectival form ends in
-ous.