Nth Root Calculator
Compute the nth root of any number — square root, cube root, fourth root and beyond — with negative-base cases handled correctly.
How it works
nth root of x = x^(1/n) — the value r such that rⁿ = x
The nth root of a number x is the value that, raised to the power n, gives back x. It is the same as raising x to the power 1/n. Even roots (square, fourth, …) of a negative number have no real value because an even power is always non-negative, while odd roots (cube, fifth, …) handle negatives fine and stay negative.
Worked example
The fourth root of 81 is the number that, multiplied by itself four times, gives 81. Since 3⁴ = 81, the fourth root of 81 is 3. Equivalently, 81^(1/4) = 3.
Sources: Nth root — Wikipedia
Frequently asked questions
Why can’t I take an even root of a negative number?
Any real number raised to an even power is zero or positive, so no real number to the 2nd, 4th, 6th … power can equal a negative. Such roots only exist in the complex numbers, which this tool does not cover.
Does a positive number have two square roots?
Yes — every positive number has a positive and a negative real root for an even degree (3 and −3 both give 9 when squared). This calculator reports the principal (positive) root and notes the negative one.
How do I get a cube root or fifth root?
Set the root degree to 3 for a cube root, 5 for a fifth root, and so on. Odd degrees accept negative values, so the cube root of −27 is −3.
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This calculator is for educational purposes. Double-check important results before acting on them.