approximate vs work out

approximate is an adjective but work out is not an adjective.

Word	Noun	Adjective	Verb	Adverb
approximate	No	Yes	Yes	No
work out	No	No	Yes	No

As verbs, work out is a hypernym of approximate; that is, work out is a word with a broader meaning than approximate:

Other hypernyms of approximate include calculate, cipher, compute, cypher, figure, reckon.

approximate (verb)	work out (verb)
judge tentatively or form an estimate of (quantities or time)	do physical exercise
be close or similar	give a workout to
	come up with
	work out in detail
	find the solution to (a problem or question) or understand the meaning of
	make a mathematical calculation or computation
	be calculated
	happen in a certain way, leading to, producing, or resulting in a certain outcome, often well