Nth root

An nth root of a number is a number whose nth power equals it. Depending on the domain and the exponent, a number can have multiple roots, one root, or none.

Exponentiation: The operation of raising a number to a power by repeated multiplication or its extensions. Finding an nth root reverses exponentiation: the root raised to n must recover the original number.
Integer: A whole number, including zero and negative whole numbers. Integer exponents and integer radicands provide the basic setting for many root questions.
Quadratic equation: An equation in one variable whose highest power is two. Solving it often requires square roots, and its discriminant determines whether those roots are real.
Square root: A number whose square equals a given number. It is the degree-two case, with familiar sign and principal-value conventions.
Principal root: The conventionally selected root, usually the nonnegative real root when the degree is even. It distinguishes the standard radical value from the other solutions of the power equation.
Real number: A number representing a point on the continuous number line. Restricting roots to real numbers explains why some even roots of negative numbers do not exist.
Distance formula: A formula for the distance between points using the square root of summed squared coordinate differences. Euclidean distance is a square root of the sum of squared coordinate differences.
Reciprocal: The multiplicative inverse of a nonzero number. Taking a reciprocal reverses multiplication, whereas taking a root reverses a power.
Complex number: A number expressible as a real part plus an imaginary part. Complex numbers supply roots when a real number system has none and reveal multiple solutions.
Even and odd numbers: Integers divisible by two are even; integers not divisible by two are odd. Whether the index is even or odd controls real-root existence for negative radicands.

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