If No route match then redirect to root page

Make this statement the last in your config/routes.rb file:

match "*path" => redirect("/")

The "*path" will match anything and will redirect to the root path.

For more info, take a look at route globbing and redirection in the official Rails guides.

In Rails 4/5 you can

get '*path' => redirect('/')

Edit. As pointed out by @VenkatK this should be last route. The way routes ere evaluated is that those on top are more important than those on the bottom.