root on vs encourage

root on and encourage both are verbs.

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

As verbs, encourage is a hypernym of root on; that is, encourage is a word with a broader meaning than root on:

root on (verb)	encourage (verb)
spur on or encourage especially by cheers and shouts	spur on
	inspire with confidence; give hope or courage to
	contribute to the progress or growth of