root on vs cheer

root on is not a noun while cheer is a noun.

Word	Noun	Adjective	Verb	Adverb
root on	No	No	Yes	No
cheer	Yes	No	Yes	No

As verbs, root on and cheer are synonyms defined as:

Other synonyms of root on include barrack, exhort, inspire, pep up, urge, urge on.

root on (noun)	cheer (noun)
	the quality of being cheerful and dispelling gloom
	a cry or shout of approval

root on (verb)	cheer (verb)
spur on or encourage especially by cheers and shouts	become cheerful
	spur on or encourage especially by cheers and shouts
	show approval or good wishes by shouting
	cause (somebody) to feel happier or more cheerful
	give encouragement to