This is the 14227th most frequent Russian word.
осмелившись
Having dared.
In this instance, the word signifies the emotional action preceding the actual approach and conversation.
Осмелившись подойти, мальчик наконец поговорил с учителем.
Having dared to approach, the boy finally talked to the teacher.
It is used as a participle to convey the act of daring before the main action.
Осмелившись, она открыла дверь и вошла внутрь.
Having dared, she opened the door and stepped inside.
Here, 'осмелившись' describes the preliminary action of daring linked to asking the question.