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From Biology-Online Dictionary | Biology-Online Dictionary
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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. (Science: mathematics) Not capable of being exactly expressed by an integral number, or by a vulgar fraction; surd; said especially of roots. See surd.

Synonym: absurd, foolish, preposterous, unreasonable, senseless. See absurd.

Origin: L. Irrationalis: cf. F. Irrationnel. See In- not, and rational.