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irradiate to expose to radiation, esp. as a medical treatment. [3 definitions]
irradiation emission of electromagnetic radiation, or the state of being exposed to such radiation. [2 definitions]
irrational lacking in reason, sense, or judgment. [3 definitions]
irreclaimable impossible to reclaim, redeem, or reform.
irreconcilable not capable of being brought into harmony or agreement; incompatible. [2 definitions]
irrecoverable not capable of being recovered or regained; irretrievable. [2 definitions]
irredeemable not capable of being bought back or paid off; not redeemable. [3 definitions]
irredentist a person who advocates annexing or recovering territories bordering his or her own country, because their populations have strong ties to his or her country's people.
irreducible not capable of being reduced to a simpler or smaller condition, form, or quantity.
irrefragable impossible to refute or dispute; undeniable.
irrefutable impossible to refute or disprove; indisputable.
irregular uneven in shape, arrangement, surface, or the like. [10 definitions]
irregularity the condition or quality of being irregular. [3 definitions]
irrelevance the quality or condition of not being related or connected to the matter or situation at hand. [2 definitions]
irrelevant not related to or connected with the matter or occasion at hand.
irreligious not practicing or believing in any religion; not motivated by religious considerations or precepts. [2 definitions]
irremediable impossible to cure, repair, or correct.
irremissible not subject to forgiveness; unpardonable. [2 definitions]
irremovable impossible to remove or obliterate.
irreparable impossible to repair, restore, or rectify.
irreplaceable impossible to replace or duplicate.