This is the 3885th most frequent Russian word.
братском
"Братском" is the prepositional case form of "братский," meaning "brotherly" or "fraternal."
The word 'братском' is an adjectival form meaning 'fraternal' and is used here to describe the union among nations as characterized by feelings of camaraderie and mutual support.
В братском союзе народы добиваются мира.
In a fraternal union, nations achieve peace.
Here 'братском' describes the house as a place characterized by a fraternal sense of community, highlighting mutual support and fond relationships among its residents.
Мы живем в братском доме, где все помогают друг другу.
We live in a fraternal house where everyone helps each other.
In this example, 'братском' characterizes the class environment as fraternal, emphasizing friendly and supportive interpersonal relations within the group.