In woodworking, that's a different word. In "english" English, the woodworking word is prononced "raowting", as in "now" or "about"; the business of choosing a route is pronounced "rooting", as in "boot".

In American English, "route" and "about" have the same vowel-sound, which seems unfortunate; I wonder how that happened.

English is a mess, but I hope we don't try to fix it!