check out vs cheque

check out is not a noun while cheque is a noun.

Word	Noun	Adjective	Verb	Adverb
check out	No	No	Yes	No
cheque	Yes	No	Yes	No

As verbs, check out and cheque are synonyms defined as:

check out (noun)	cheque (noun)
	a written order directing a bank to pay money

check out (verb)	cheque (verb)
examine so as to determine accuracy, quality, or condition	withdraw money by writing a check
announce one's departure from a hotel
try to learn someone's opinions and intentions
record, add up, and receive payment for items purchased
withdraw money by writing a check
trace
be verified or confirmed; pass inspection