incoherent vs irrational

incoherent is not a noun while irrational is a noun.

Word	Noun	Adjective	Verb	Adverb
incoherent	No	Yes	No	No
irrational	Yes	Yes	No	No

incoherent (noun)	irrational (noun)
	a real number that cannot be expressed as a rational number

incoherent (adjective)	irrational (adjective)
without logical or meaningful connection	not consistent with or using reason
(physics) of waves having no stable definite or stable phase relation	real but not expressible as the quotient of two integers
unable to express yourself clearly or fluently