Root Calculator - Find Any Nth Root

An nth root reverses exponentiation. The nth root of a number x is the value that, when multiplied by itself n times, equals x. The number x is called the radicand and n is called the index or degree. A degree of two gives the familiar square root, a degree of three gives the cube root, and any positive whole-number degree defines a corresponding higher root. The calculation can be written as x raised to the power of one divided by n. For positive radicands, that rule works directly for every positive integer degree. For example, the fourth root of 81 is 3 because 3 raised to the fourth power is 81. Most roots are irrational decimals, so the calculator carries full floating-point precision and rounds only the displayed result to a practical length. Negative radicands need special attention in the real-number system. An odd power preserves the sign, so the cube root of negative 125 is negative 5. An even power cannot produce a negative real value, so an even root of a negative number has no real result. Complex-number roots do exist, but this calculator deliberately reports real principal roots and identifies inputs that would require complex arithmetic. Roots appear throughout algebra, geometry, science, statistics, and engineering. Square roots recover a side length from an area, feature in the distance formula and quadratic formula, and convert variance to standard deviation. Cube roots recover dimensions from volume. Higher roots reverse compound growth across several periods and solve equations involving powers. Be aware that every positive number has two square-root solutions when solving the equation y squared equals x: positive and negative. The radical symbol and this calculator conventionally return the principal, nonnegative square root. For odd roots there is one real root, whose sign matches the radicand. A radicand of zero always has a root of zero for every permitted degree. To verify a result, raise the displayed root to the entered degree. Tiny differences may appear for irrational values because computers represent decimals with finite binary precision. These differences are normal and do not affect typical educational or professional calculations. When a final answer depends on measured data, round according to the precision of the original measurements rather than the maximum number of digits shown.