First, to clear the error, you need to use named routes :
put 'approve_class_room/:id(.:format)', :to => 'class_room_member_ships#approve',
:as => :approve_class_room
put 'reject_class_room/:id(.:format)', :to => 'class_room_member_ships#reject',
:as => :reject_class_room
Then, to execute the PUT request, you need to include the parameter :methodin your call link_to:
link_to 'approve', approve_class_room_path, :method => :put
link_to 'reject', reject_class_room_path, :method => :put
404, GET PUT, , :method => :put JavaScript. , jquery-rails .