irrational vs incoherent

irrational is a noun but incoherent is not a noun.

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

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

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