Just saying it in my head makes me crack up
Wireless root-er .... hahahahahaha !!! Sorry
Btw, I have a heavily British influenced education (up to secondary school) .
Route = root
Router = rowter
row-ooteh.
Yes, and god is an iron...Why do you think that something that routes (roots) packets is called a router (root-er) ?
One is obviously derived from the other, and yet you decide to pronounce the second one differently.
Don't you say that something that digs is called a digger? Something that flies a flyer? Someone that begins a beginner? You don't change the pronunciation of the root (ha!) word just because you turn it into "-er".