Ir*ra"tion*al (?), a. [L. irrationalis: cf. F. irrationnel. See In- not, and Rational.]

1. Not rational; void of reason or understanding; as, brutes are irrational animals.

2. Not according to reason; absurd; foolish.

It seemed utterly irrational any longer to maintain it.

3. (Math.) Not capable of being exactly expressed by an integral number, or by a vulgar fraction; surd; -- said especially of roots. See Surd.

Syn. -- Absurd; foolish; preposterous; unreasonable; senseless. See Absurd.

• Not rational; unfounded or nonsensical.
       an irrational decision
  
• (mathematics) (no comparative or superlative) Of a real number, that cannot be written as the ratio of two integers.
       The number π is irrational.