This is the 10137th most frequent Russian word.
безопасных
"Safe" (genitive plural or accusative plural form).
The word 'безопасных' is used as an adjective describing 'маршрутов', modifying it to mean 'safe' in the plural genitive case.
Мы выбираем только безопасных маршрутов для прогулок.
We choose only safe routes for walks.
Here, 'безопасных' modifies 'игр', signifying that the games are safe, using the plural genitive case again as the context concerns conditions.
Важно обеспечить условия для безопасных игр детей.
It's important to provide conditions for the safe play of children.
In this example, 'безопасных' is linked to 'методов', describing them as safe, using the plural genitive case for contextual accuracy.