Rationalizes

Rationalizes is the third-person singular present tense form of the verb rationalize. It has two broad senses: mathematical operations to remove radicals from denominators or simplify expressions, and psychological or everyday usage to provide reasons or justifications for actions or beliefs. In mathematics, rationalizing an expression means transforming it into an equivalent expression without irrational denominators, often by multiplying by a suitable factor.

A common technique is multiplying by a conjugate; for example, 1/(a+√b) × (a−√b)/(a−√b yields (a−√b)/(a²−b). This process can also be applied to more complex expressions or fractions to eliminate radicals from the denominator, and sometimes to rationalize numerators.

In psychology and everyday language, rationalizing describes giving plausible but potentially misleading justifications for behavior, often to reduce cognitive dissonance or to mask true motives. It can also refer more broadly to presenting something as more rational or efficient than it originally appears, even if the underlying reasoning is incomplete or self-serving.

Etymology and related concepts: rationalizes derives from Latin ratio, meaning reason, with the suffix -ize. Related terms include rationalization, ratio, and rational. In mathematical contexts, related operations include simplification, conjugation, and radical manipulation.