Add - before google_api/auth/callback

config/routes/google_api.rb

-namespace :google_api do
-  resource :auth, only: [], controller: :authorizations do
-    match :callback, via: [:get, :post]
+scope '-' do
+  namespace :google_api do
+    resource :auth, only: [], controller: :authorizations do
+      match :callback, via: [:get, :post]
+    end
   end
 end