My dad was wondering about this earlier today while we were watching a football game.
How did the word “root” acquire its meaning as a synonym for “cheer”? We can say “I’m cheering for this team” and “I’m rooting for this team” and have it be the same thing. How can a word like root get this kind of meaning?
It doesn’t have the same meaning in Australia…
In fact, to say you’re “rooting” for the team is bound to bring some stifled giggles.
Australians “barrack” for teams. I’ve never heard that word in use in the US.
My American Heritage say it’s probably an alteration of the word rout - meaning, “to make a loud noise or clamor.”
Chambers, in his Dictionary of Etymology says:
Verb, "Cheer or support a contestant, etc. 1889, American English; probably derived from earlier sense of root(verb), to study or work hard(1856).
C’mon Cazzle, we Aussies are more mature than to giggle at such thi… ppffffffft! 
Perhaps the Canadians are responsible for changing rout to “root” 
I have no idea what you’re talking aboot.
That is the case in Victoria but I’m not sure about other parts of the country. Originally, barrack meant the opposite; to disparage and jeer. I’ve heard some sporting venues in Britain have signs saying, “Please, no barracking”…