In my lab today we had a discussion over the proper way to say the word "Route" dictionaries and professional linguists who were consulted give both "root" and "rout" as acceptable pronunciations, leaving us no wiser than before.
But online, we find this Dialect survey (color matching the map).
"26. route (as in, "the route from one place to another")
a. rhymes with "hoot" (29.99%)
b. rhymes with "out" (19.72%)
c. I can pronounce it either way interchangeably (30.42%)
d. I say it like "hoot" for the noun and like "out" for the verb. (15.97%)
e. I say it like "out" for the noun and like "hoot" for the verb. (2.50%)
f. other (1.40%)
As a north-easterner myself, It was always take Root 29 or Root 95, but in the South, we were on Rout 85. In the midwest, it seems more Rout than Root. In any case the "e" is superfluous, as it doesn't modify in a consistent way, since we already have a double vowel. The word is also superfluous, since we already have the word "road" from the same root. Damn French imports.
Etymology online says: route (n.) early 13c., from O.Fr. rute "road, way, path," from L. rupta (via) "(a road) opened by force," from rupta, fem. pp. of rumpere "to break" (see rupture). Sense of "fixed or regular course for carrying things" (cf. mail route) is 1792, an extension of the meaning "customary path of animals" (early 15c.).
See also this on Highway Linguistics