いったい
what on earth, (who / where / why) on earth
いったい + question word … (のだろう · のか)
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いったい strengthens a question, adding surprise, frustration or bewilderment: いったい何があったんですか, "what on earth happened?"
It always comes with a question word: 何, 誰, どこ, どうして, いくら, どう. The sentence often ends with のだろう, んだろう or の: こんな時間にいったい誰だろう, "who on earth could it be at this hour?"
It's used when the speaker genuinely can't understand something, or is exasperated: いったいどこに行っていたの?, "where on earth have you been?"
Don't use it for an ordinary, neutral question. It's emphatic, and can sound accusing. In writing, it's often in kanji: 一体.
Examples
いったい何があったんですか。
What on earth happened?
こんな時間にいったい誰だろう。
Who on earth could it be at this hour?
いったいどこに行っていたの?
Where on earth have you been?
いったいいくら払ったんですか。
Just how much did you pay?
いったいどうすればいいんだろう。
What on earth am I supposed to do?