Irrational is a related term of foolish.
As adjectives the difference between irrational and foolish
is that
irrational is not rational; unfounded or nonsensical while
foolish is lacking good sense or judgement; unwise.
As a noun irrational
is a real number that can not be expressed as the quotient of two integers, an irrational number.
Other Comparisons: What's the difference?
irrational English
Adjective
( en adjective)
Not rational; unfounded or nonsensical.
 an irrational decision
* July 18 2012 , Scott Tobias, AV Club The Dark Knight Rises [http://www.avclub.com/articles/thedarkknightrisesreviewbatman,82624/]
 Where the Joker preys on our fears of random, irrational acts of terror, Bane has an allconsuming, dictatorial agenda that’s more stable and permanent, a New World Order that’s been planned out with the precision of a military coup.
(mathematics, arithmetic, number theory, not comparable) Of a real number, that cannot be written as the ratio of two integers.
 The number π is irrational .
Antonyms
* (mathematics) rational
Hyponyms
* (mathematics) transcendental
Derived terms
* irrational number
* irrationality
* irrationalize
* irrationalization
Noun
( en noun)
A real number that can not be expressed as the quotient of two integers, an irrational number.
* 1946 , (Bertrand Russell), History of Western Philosophy , I.24:
 The square root of 2, which was the first irrational to be discovered, was known to the early Pythagoreans, and ingenious methods of approximating to its value were discovered.

foolish English
Adjective
(enadj)
Lacking good sense or judgement; unwise.
:
*
*:As a political system democracy seems to me extraordinarily foolish , but I would not go out of my way to protest against it. My servant is, so far as I am concerned, welcome to as many votes as he can get. I would very gladly make mine over to him if I could.
Resembling or characteristic of a fool.
:
*(Aeschylus)
*:It is a profitable thing, if one is wise, to seem foolish .
Synonyms
* absurd
* idiotic
* ridiculous
* silly
* unwise
Antonyms
* wise
Derived terms
* foolishness
