Nth Root Calculator
MathematicsCalculate square roots, cube roots, and general real n-th roots (ⁿ√x) for positive and negative numbers with high-precision radical simplification.
About this calculator
Evaluating radical expressions is fundamental in algebra, geometry (Pythagorean distance), physics (escape velocity), and finance (geometric mean compound growth rates).
This calculator evaluates ⁿ√x for any positive integer or fractional degree n. For odd roots (n = 3, 5, 7...), it properly evaluates real roots of negative radicands (e.g. ³√(-8) = -2), and verifies results through exponential powers.
How It Works & Formula
The n-th root of x is mathematically equivalent to x^(1/n). The calculator computes exp((1/n) * ln(x)) with special sign handling for negative bases with odd integer exponents.
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