Does anyone find it ironic that Americans have this stereotypical view that Canadians pronounce the word 'about' as 'aboot' (I've never actually heard anyone pronounce it that way) yet most of them pronounce 'route' as 'root'? I mean, they don't pronounce 'router' as 'rooter' so why would they pronounce 'route' as 'root'?
Prouncing 'route'
root is the correct pronunciation of 'route'. It's a word of French origin. And I seem to hear /ɻaʊt/ more often then 'root' in America so I don't know where you got that info from. And Canadians do pronounce 'about' as "a boat". "aboot" is a funny exaggeration.
Americans may pronounce neither - nuyther while pronouncing either - eether too, that doesn't mean anything.