rationalize

Rationalize is a verb with several related senses in English. In everyday language, it means to make something more rational by applying reason, or to justify actions by presenting acceptable explanations, sometimes post hoc. It can also refer to reorganizing processes to improve efficiency or consistency, a use common in business and administration.

In mathematics, rationalize refers to transforming expressions to remove irrational components, especially removing radicals from denominators. The classic operation is to multiply numerator and denominator by a suitable radical or conjugate so the denominator becomes rational. Rationalization is a standard technique in simplifying expressions and in evaluating limits or integrals where radicals appear.

In psychology, rationalization is a defense mechanism whereby a person fabricates or selects plausible-sounding explanations to justify unacceptable thoughts, feelings, or actions, often masking true motives. It is distinguished from genuine logical reasoning because the justification is primarily to reduce cognitive dissonance rather than to converge on truth.

In economics, industry, and public administration, rationalization denotes reorganizing or standardizing production and administrative processes to improve efficiency, reduce redundancy, and lower costs. It may involve consolidating roles, updating technology, or streamlining workflows, sometimes facing resistance from stakeholders.

Etymology: from Latin ratio, reason, and the suffix -ize. First used in English in the 17th century in the sense of applying reason, later extended to mathematical use and to organizational practices. Examples include rationalizing a denominator in algebra and rationalizing production in a factory.