hellish
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hellish / extremely
Used colloquially as an intensifier meaning 'extreme,' 'very,' or 'enormous.' It is mostly used for negative sensations such as pain, difficulty, or noise.
Nach dem Unfall hatte er höllische Schmerzen im Bein.
After the accident, he had hellish pain in his leg.
The adjective 'höllisch' (hellish) is derived directly from the noun 'die Hölle' (hell). So originally it describes something that belongs to hell or is like hell.
Der Lärm aus der Fabrik war einfach höllisch.
The noise from the factory was simply hellish.
The literal, religious meaning is rare. You can recognize it in a context involving religion or mythology. In almost all other cases, the colloquial meaning 'extreme' is intended.
Der Priester warnte vor dem höllischen Feuer.
The priest warned of the hellish fire.
In everyday language, 'höllisch' (hellish / extremely) is usually used as a colloquial intensifier for 'very' or 'extreme,' almost always in a negative context.
Ich habe höllischen Hunger.
I'm incredibly hungry.
As an intensifier, 'höllisch' (hellish / extremely) is often combined with negative sensations or conditions: 'höllische Schmerzen' (hellish pain), 'ein höllischer Lärm' (a hellish noise), 'höllische Angst' (terrible fear), or 'höllisch kalt' (extremely cold).
Wegen des Unfalls war die Autobahn höllisch voll.
Because of the accident, the highway was extremely crowded.
extreme
'extrem' and 'höllisch' can both describe something very strong or intense. 'extrem' is general and can fit many topics, including neutral ones. 'höllisch' is colloquial and is used especially for unpleasant things, for example pain, noise, heat, or difficult work. It sounds more vivid and stronger than a normal 'sehr' (very). If you want to stay factual, 'extrem' fits better; if you want to express a strong negative sensation, 'höllisch' works well.
Nach dem Training tun mir die Beine höllisch weh.
After training, my legs hurt like hell.
Die Wartezeit beim Arzt war extrem lang.
The wait at the doctor's office was extremely long.