I came across this sentence in an exercise, so there is no context :
こんなに寒い部屋によく住めるね。
What is exactly the meaning of よく住める and is it possible to have one or two other sentences using it?
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Sign up to join this communityHere よく means how (can/do you) ...?, indicating the speaker thinks '...' is something extraordinary. It is somewhat close to how come ...?.
So the sentence means how can you live in such a cold room like this? (I think it's impossible).
Incidentally よく can be put at the front: よくこんな寒い部屋に住めるね.
Other examples:
Note that it often comes with そんな/こんな or なんか (roughly corresponding to such).
デジタル大辞泉 lists this usage of よく(well) as separate definitions:
4 困難なことをしたり、考えられないような喜ばしい結果を得たりして感じ入るさま。本当にまあ。よくぞ。「―来てくれました」「月給だけで―やっていけるね」
5 相手の非常識な言動などを非難するさま。4を反語的にいう語。よくもまあ。「―のこのこと来られたものだ」
5 is the definition for how dare...
That said, I suppose it can be understood as an exclamation. E.g. the sentence in question is how well you live in such a cold room! and the speaker thinks you are doing too well (much).
In terms of register, it is colloquial, but can be made polite. E.g. よくこんな寒い部屋に住めますね.
Ending with な (e.g. 住めるな) would sound masculine and somewhat more rude.