Learn Hardcore Korean: doseogwaneseo keompyuteoreul iyonghae bwasseoyo. - I tried using the computer at the library.

도서관에서 uses the particle -에서 to mark the place where the action happens (“at the library”). If you said 도서관에, that would mark a destination or static location (“to the library” or “in the library” with verbs like 있다/가다), but not the site of the action. So for “I did something at the library,” you need 도서관에서.

Why is it 컴퓨터를 이용해 봤어요 instead of 컴퓨터를 이용했어요?

The ending -아/어 보다 after a verb means “to try doing” that action.
– 이용해 봤어요 = “I tried using/utilizing (the computer).”
– 이용했어요 = “I used/utilized (the computer)” with no nuance of “trying it out.”

How is 이용하다 different from 사용하다 or 쓰다?

– 이용하다 (利用–) is like “to make use of,” often for services, facilities, systems, tools in a somewhat formal register.
– 사용하다 (使用–) simply means “to use” in a general sense.
– 쓰다 can mean “to use,” “to write,” or “to wear,” depending on context, and is more colloquial.
So at a library, 컴퓨터를 이용하다 sounds natural if you treat the computer as a facility.

Why is the computer marked with -를 (object particle) and not -로 (instrumental)?

When you say 컴퓨터를 이용하다, 컴퓨터 is the direct object of 이용하다 (“to utilize X”). If you wanted to say “searched using the computer,” you might say 컴퓨터로 검색했어요, where -로 marks the means/instrument because 검색하다 is the main verb and the computer is the tool.

What exactly does -아/어 보다 do grammatically, and why is 봤어요 used here?

-아/어 보다 attaches to a verb stem to give the sense “try doing [verb].” The verb 보다 itself is then conjugated to the desired tense/politeness. Here, 이용해 + 보다 → 이용해 보다, and in past polite form it becomes 이용해 봤어요.

What level of politeness is 봤어요, and how could I change it?

-았/었어요 is polite informal speech (the “yo” ending polite form).
– More formal: 이용해 보았습니다
– Casual/friendly: 이용해 봤어 / 이용해 봤다 (plain style)

What nuance difference is there between 컴퓨터를 이용해 봤어요 and 컴퓨터를 써 봤어요?

– 컴퓨터를 써 봤어요 is casual and everyday (“I tried using the computer”).
– 컴퓨터를 이용해 봤어요 sounds slightly more formal or official, emphasizing “utilizing the facility/service.” Both mean you tried using a computer, but 이용하다 carries a nuance of “making use of (a resource).”