By - marcireneej
It means, "you have to/should drink milk!" and it's informal. 우유 마셔야죠 is more polite.
This was in a children's workbook so I guess that's why it's informal. Is this an imperative format?
Not a linguist but wouldn’t this be subjunctive mood since you’re expressing your desire
The subjunctive in many languages expresses mood and doubt. In English, it is translated generally by may.
English doesn't have a subjunctive as such. It has subjunctive clauses, but no special subjunctive verb form. May and might are modal verbs.
Prefacing this by saying I'm not fluent by any measure so I could be wrong here.
It means '(you) must/should drink milk' with 'you' being implied.
우유 - milk
마시다 + 어/아/여야지 - drink + (you) must/should
It's informal so if you wanted to say that specific sentence politely perhaps 우유를 마셔야지요. But to be honest that's still kinda forcefull in my opinion. Perhaps a more fluent speaker could give a better substitute (I'm just an intermediate learner).
But if you want to say 'drinking milk' (rather than 'you must drink milk' in a polite way, I'm gonna need more context.
[this link](https://www.howtostudykorean.com/unit-2-lower-intermediate-korean-grammar/unit-2-lessons-42-50/lesson-46/?amp) explains it completely. It’s a combination of two grammar features, ~아/어 하다/되다 (have to/should) and ~지 (used for emphasis) and it’s 반말, simply adding ~요 (contracted form ~죠) would make it formal
It is a grammar that is similar to "당연하다" like "of course you need to do this" but it is not brusque or negative, it kind of reinforces the meaning. In this case it means "you need to drink your milk (you know it)". 죠 is more polite.
It is very common to say "당연하지", as "of course" "consider it done" "you got it"