Radical

Radical is a term with several related but distinct meanings across mathematics, science, linguistics, and politics. It ultimately derives from the Latin radix, meaning "root," reflecting a focus on origins or fundamental aspects.

In mathematics, a radical denotes a root of a number or expression, shown by the radical symbol (√) or by an index, as in square roots and nth roots. Radicals can be simplified, combined, or placed in equations; the term also appears in geometry as the radical axis of circles.

In chemistry, a radical is an atom or molecule with an unpaired electron, making it highly reactive. Examples include the hydroxyl radical (OH) and the methyl radical (CH3). Radicals drive combustion and polymerization and participate in atmospheric chemistry; living systems generally try to limit damaging radicals with antioxidants.

In linguistics, radical can mean the root or base form of a word. In many languages, especially in East Asia, "radical" designates a root component used to classify characters in dictionaries.

In political and social discourse, a radical is a person or idea advocating substantial, fundamental reform to institutions or norms. The label is value-laden and context-dependent, sometimes signifying reformist aims and other times implying extremism.