Irreducible \Ir`re*du"ci*ble\, a.

1. Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.

2. (Math.) Incapable of being reduced to a simpler form of expression; as, an irreducible formula.

Irreducible case (Alg.), a particular case in the solution of a cubic equation, in which the formula commonly employed contains an imaginary quantity, and therefore fails in its application. -- Ir`re*du"ci*ble*ness, n. -- -- Ir`re*du"ci*bly, adv.

Source: Webster's Revised Unabridged Dictionary (1913)