Learn Spanish (Latin America): Investigaste tu apellido hace un mes. - You researched your last name a month ago.

In Spanish, the formula hace + [amount of time] is used to say how long ago a completed action happened. Even though hace comes from the verb hacer (to do/make) and literally translates to "it makes," in this time expression, hace un mes simply means "a month ago."

Could I put "hace un mes" at the beginning of the sentence instead?

Yes, you can! You could say Hace un mes, investigaste tu apellido. Moving the time expression to the front is very common in Spanish and doesn't change the meaning of the sentence at all.

How do we know to use the preterite tense "investigaste" instead of the imperfect?

The phrase hace un mes (a month ago) acts as a specific time marker. Because it points to a single action that started and finished in the past, it triggers the preterite tense (investigaste) rather than the imperfect tense, which is used for ongoing or repeated past habits.

Is "apellido" related to the English word "apology"?

No, this is a classic "false friend"! Apellido only means "last name" or "surname." If you want to say "apology" in Spanish, you would use a word like disculpa.