borrowed from Middle French route "defeat, disorderly retreat," noun derivative from feminine of rout, alternate past participle of rompre "to defeat, put to flight," literally, "to break, smash," going back to Old French, going back to Latin rumpere — more at route entry 1
Middle English route "group, band of soldiers, crowd," borrowed from Anglo-French route, rute "band, herd, armed force," going back to Vulgar Latin *rupta "detachment," literally, "something broken off," going back to Latin, feminine of ruptus, past participle of rumpere "to break" — more at route entry 1
Verb (2)
presumed to be variant of wroot,root entry 3 (though alteration of vowel is unexplained)
Verb (3)
Middle English (northern) & early Scots rowten, rowte, borrowed from Old Norse rauta "to roar," going back to Germanic *rautōjan-, probably derivative of a noun *raut- "bellowing, roaring," from an ablaut derivative of *reutan- (whence Old English rēotan "to weep, wail," Old High German riozan "to weep, mourn," Old Swedish riuta "to roar"), going back to Indo-European *Hreu̯d- "produce a loud sound, weep," whence, with varying ablaut grades, Latin rudere, rūdere "to make a loud noise, bellow, bray," Lithuanian raudóti "to sob, weep," Old Church Slavic rydati, Sanskrit rodiṣi "(you) weep"