1. Contraction of the phrase "rock out."
2. To go out, spend lots of money, drink lots of booze, and shamelessly hit on girls. Essentially, to get nice and go huge.
notes: "rout" is commonly used together with the word "cout" which is itself a contraction of the words "cock out." Routing is also an important concept in the Get Drunk and Go for It school of thought.
Ben: Yeah, let's take many tequila shots and rout with our couts.
James: Did you get nice last night?
Ben: I straight routed; I gave some girl all kinds of orgasms when I put my d in her v.