
betrunken
drunk
Being in a state in which behavior and perception are affected by the consumption of alcohol.
Nach drei Bier war er schon sichtlich betrunken.
After three beers, he was already visibly drunk.
drunk
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drunk
Being in a state in which behavior and perception are affected by the consumption of alcohol.
Nach drei Bier war er schon sichtlich betrunken.
After three beers, he was already visibly drunk.

drunk with
In a figurative sense, to be overwhelmed and intoxicated by a strong feeling such as success, happiness, or love.
Sie war betrunken vor Glück, als sie die Zusage für den Job erhielt.
She was drunk with happiness when she received the job offer.
'Betrunken' (drunk) is the past participle of the reflexive verb 'sich betrinken' (to get drunk). It is almost always used as an adjective to describe a state.
Er hat sich auf der Party gestern Abend ziemlich betrunken.
He got pretty drunk at the party last night.
'Betrunken' (drunk) is usually combined with the verbs 'sein' (to be, state) or 'werden' (to become, process).
Pass auf, dass du nicht zu schnell betrunken wirst.
Be careful that you don't get drunk too quickly.
The word 'betrunken' (drunk) is the neutral standard expression. It can be used both in everyday conversations and in more formal contexts, such as a police report.
Der Fahrer des Wagens war zum Unfallzeitpunkt betrunken.
The driver of the car was drunk at the time of the accident.
In the figurative sense, 'betrunken' (drunk) is always used with the preposition 'von' and a feeling or abstract concept in the dative. It describes a state of emotional overwhelm.
Er war betrunken vom Erfolg und fühlte sich unbesiegbar.
He was drunk with success and felt invincible.
full
Both words can describe a state resulting from drinking a lot of alcohol. „Betrunken“ is the neutral and unambiguous term. „Voll“ is very colloquial in this meaning, usually suggests a high degree of intoxication, and can mean something else without clear context.

Nach der Feier war er so betrunken, dass er ein Taxi nach Hause nahm.
After the party, he was so drunk that he took a taxi home.
Nach der Feier war er so voll, dass er ein Taxi nach Hause nahm.
After the party, he was so drunk that he took a taxi home.