The Collaborative International Dictionary of English v.0.48:

irrational \ir*ra"tion*al\ ([i^]r*r[a^]sh"[u^]n*al), a. [L.
   irrationalis: cf. F. irrationnel. See In- not, and
   Rational.]
   [1913 Webster]
   1. Not rational; void of reason or understanding; as, brutes
      are irrational animals.
      [1913 Webster]

   2. Not according to reason; having no rational basis; clearly
      contrary to reason; easily disproved by reasoning; absurd;
      -- of assertions and beliefs. Hence, of actions: foolish;
      unreasonable.
      [1913 Webster +PJC]

            It seemed utterly irrational any longer to maintain
            it.                                   --I. Taylor.
      [1913 Webster]

   3. (Math.) Not capable of being exactly expressed by an
      integral number, nor by a ratio of integral numbers; surd;
      -- said especially of roots. See Surd.

   Syn: Absurd; foolish; preposterous; unreasonable; senseless.
        See Absurd.
        [1913 Webster]

WordNet (r) 3.0 (2006):

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]
    n 1: a real number that cannot be expressed as a rational number
         [syn: irrational number, irrational]