Nth Root Calculator — Square & Cube

The nth root of a number x is the value that, when raised to the power n, gives x. It is the inverse operation of exponentiation: if yⁿ = x, then y = ⁿ√x = x^(1/n). While square and cube roots are the most commonly needed, higher-order roots appear in signal processing, physics, statistics, and financial mathematics.

For positive radicands, any positive integer root exists as a real number. For negative radicands, only odd roots exist in the real number system — e.g., the cube root of −8 is −2. Even roots of negative numbers (like √(−4)) require complex numbers and are not computed by this tool.

Practical applications of nth roots include finding the geometric mean (nth root of a product of n numbers), computing compound growth rates (nth root of cumulative return), solving polynomial equations, and working with logarithmic scales. The calculator handles fractional n as well, computing arbitrary power roots.