Abarim Publications' online Biblical Greek Dictionary
The verb γευω (geuo) means to taste or give to taste. It stems from the same Proto-Indo-European root "gews-", to enjoy or taste, that gave English the verb to choose.
Taste is of course one of the senses, but unlike seeing and hearing, taste is a sense that allows the consumer to try something out before it is accepted and swallowed. When something doesn't taste right, it can be spat out (Matthew 27:34, Revelation 3:16), which means that taste has to do with discernment, preference and selection (1 Peter 2:3), and not wanting to taste anything is the same as not wanting to listen to alternatives or explanations (Acts 23:14).
Note that the celebrated noun sapiens is actually the present active participle of the Latin verb sapio, to discern by taste: to have good taste.
Our verb γευω (geuo) is used 15 times in the New Testament; see full concordance. No derivations of this verb are used.