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Boscopher is not entirely correct with Korean translation. Here are some Korean nouns and definitions:
  • "Han-guk" = Korea (literally: Han country)
  • "Han-guk-in" = Korean people/person (literally: Han country people/person)
  • "mi-guk" = USA (literally: beautiful country)
  • "mi-guk in" = "American" people/person (literally: beautiful country people/person)
Here, Han is different from the ancient Han dynasty of China, and uses different characters. Names of most countries end with a country character as a suffix: "guk" in Korean, "guo" in Chinese, "koku/goku" in Japanese, and I suppose a similar system might also exist for Vietnamese. The Chinese-origin morpheme for "person/people" is "in" while the Korean-native word for it is "sharam."

The slang "gook" in American-English is a derogatory term for East Asians. What the dictionaries have to say about the origin is also note-worthy.

American Heritage dictionary says:
Perhaps alteration of earlier goo-goo, native inhabitant of the Philippines, Pacific islander.
The current version of Webster says:
Origin unknown