Where does “разговорить” come from?

разговорить (Russian) comes from Russian раз-, from Old East Slavic роз-, from Proto-Slavic orz- — dis-.

Ancestry of “разговорить”, step by step

Step	Language	Word	Meaning
1	Russian	раз-	asunder, apart; dis-, di-, un-; enlarged action
2	Old East Slavic	роз-	—
3	Proto-Slavic	orz-	dis-

разговорить — Etymology, Origin & Word History | Etymology Explorer