Radicaalteken

Radicaalteken, in Dutch often called the radical sign, is a mathematical symbol used to indicate the operation of taking roots. The most common root is the square root, written as √x, which denotes the nonnegative number y such that y² = x. For nonnegative real numbers x, √x is real; for negative x, the square root is not a real number.

An index on the radical denotes an nth root, as in ∛y for the cube root or ⁴√z for the fourth root, with the general form √[n]{a}. The nth root is equivalent to a raised to the power 1/n (a^(1/n)). Radicals appear in algebra, geometry, calculus, and many applied fields, in tasks such as solving equations, simplifying expressions, and evaluating integrals.

Notation and encoding: The radical sign is encoded in Unicode as U+221A and can be represented in plain text as sqrt or with explicit index notation in mathematical typesetting. In LaTeX, for example, one writes \\sqrt{ } and, for an nth root, \\sqrt[n]{ }.

History and interpretation: The radical sign began appearing in early modern European mathematics in the 16th century and is generally thought to derive from a stylized representation related to the word radix (root) or from a check-mark style symbol used in older notations. The exact origin is not definitively established.

Mathematical properties: For nonnegative radicands, √a is defined as the principal root, satisfying (√a)² = a. In the complex numbers, every nonzero number has two square roots, and the principal value is chosen by convention. The radical sign interacts with exponents via √[n]{a} = a^(1/n).