extrem
extremely
To a very high degree; used as an intensifier for an adjective or adverb.
Das Wasser im See war extrem kalt.
The water in the lake was extremely cold.

extreme
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extremely
To a very high degree; used as an intensifier for an adjective or adverb.
Das Wasser im See war extrem kalt.
The water in the lake was extremely cold.

'Extrem' can stand as an adverb before an adjective or adverb to intensify it. In that case, it is not declined. When it stands directly before a noun as an adjective, it is declined like any other adjective.
Der Film war extrem langweilig.
The film was extremely boring.
As an adverb, 'extrem' means something like 'sehr' (very) or 'außergewöhnlich' (exceptionally). It can be used to describe the intensity of a feeling, quality, or action.
Er ist extrem intelligent.
He is extremely intelligent.
As an adjective, 'extrem' is often used to describe difficult or challenging circumstances. Common combinations are 'extreme Bedingungen' (extreme conditions), 'extreme Temperaturen' (extreme temperatures), or 'eine extreme Situation' (an extreme situation).
Die Rettungskräfte arbeiteten unter extremen Bedingungen.
The rescue workers worked under extreme conditions.
very
'sehr' and 'extrem' can both intensify something strongly. 'sehr' is more general and more neutral. 'extrem' is stronger and emphasizes that something goes especially far or is almost at the edge of what is normal. That is why 'extrem' works well with heat, cold, prices, stress, or difficult situations. Learners may confuse the words because both can stand before adjectives. But 'extrem' sounds more intense and sometimes more dramatic than 'sehr'.

Wegen der hohen Preise kaufe ich im Moment extrem wenig Kleidung.
Because of the high prices, I am buying extremely little clothing at the moment.
Frau Neumann findet den neuen Spielplatz im Park sehr schön.
Ms. Neumann thinks the new playground in the park is very nice.