Full DNS lookup of an IP using TCP for a FQDN takes 44 packets.
This includes
    Querying the local caching nameserver (11 to initiate the request and receive the answer)
    Querying the root servers (11 packets)
    Querying the tld servers (11 packets)
    Querying the authoritive name server (11 packets)

Full DNS lookup of an IP using UDP for a FQDN takes only 8 packets max.