This is the 3106th most frequent Japanese word.
何気なく
Casually; unintentionally; without much thought.
In this sentence, "何気なく" is used to convey the casual and unintentional nature of the way the words were spoken, implying the speaker did not intend to profoundly affect the listener, yet it happened inadvertently.
彼の何気なく言った言葉が、私の心に響きました。
His casually spoken words resonated with my heart.
Here, "何気なく" is used to describe the unwarranted and spontaneous action of looking out the window, emphasizing the lack of intent or focus in the action.
彼女は何気なく窓の外を眺めていた。
She was casually gazing out the window.
In this sentence, "何気なく" reflects the unplanned and incidental nature of noticing the mistake, portraying it as an act performed without deliberate observation or intervention.