Source : Webster's Revised Unabridged Dictionary (1913)

Irrational \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.                                   --I. Taylor.

   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}.

Source : WordNet®

irrational
     adj 1: not consistent with or using reason; "irrational fears";
            "irrational animals" [ant: {rational}]
     2: real but not expressible as the quotient of two integers;
        "irrational numbers" [ant: {rational}]