Nth Root Calculator
Nth Root Calculator
Enter a number and the root degree (n) you want — 2 for square root, 3 for cube root, or any higher degree. This calculates the nth root, generalizing square and cube roots to any degree.
Every nth root can be rewritten as a fractional exponent — the nth root of x is the same as x raised to the power 1/n — which is why roots and exponents are really two notations for the same underlying operation. Even-degree roots (square, 4th root, 6th root...) require a non-negative input, since no real number raised to an even power produces a negative result, while odd-degree roots (cube root, 5th root...) work fine for negative numbers, giving a negative result back.
- Formula: the nth root of x is x^(1/n) — equivalently, the value that when raised to the power n equals x.
- Even degrees need non-negative inputs: an even-degree root (2, 4, 6...) of a negative number has no real result, since no real number raised to an even power is negative.
- Odd degrees work for negative numbers too: an odd-degree root (3, 5, 7...) of a negative number has a real, negative result — e.g. the 5th root of −32 is −2.
What happens if I enter a negative number with an even root degree?
The calculator returns "undefined (no real root)" since no real number raised to an even power can produce a negative result — this case genuinely has no answer within the real numbers.
How is this different from just using a square or cube root calculator?
This generalizes to any root degree you choose, so instead of being limited to n=2 or n=3, you can find the 4th root, 7th root, or any other degree in one place.
Nth Root Calculator
Enter a number and the root degree (n) you want — 2 for square root, 3 for cube root, or any higher degree. This calculates the nth root, generalizing square and cube roots to any degree.
Every nth root can be rewritten as a fractional exponent — the nth root of x is the same as x raised to the power 1/n — which is why roots and exponents are really two notations for the same underlying operation. Even-degree roots (square, 4th root, 6th root...) require a non-negative input, since no real number raised to an even power produces a negative result, while odd-degree roots (cube root, 5th root...) work fine for negative numbers, giving a negative result back.
- Formula: the nth root of x is x^(1/n) — equivalently, the value that when raised to the power n equals x.
- Even degrees need non-negative inputs: an even-degree root (2, 4, 6...) of a negative number has no real result, since no real number raised to an even power is negative.
- Odd degrees work for negative numbers too: an odd-degree root (3, 5, 7...) of a negative number has a real, negative result — e.g. the 5th root of −32 is −2.
What happens if I enter a negative number with an even root degree?
The calculator returns "undefined (no real root)" since no real number raised to an even power can produce a negative result — this case genuinely has no answer within the real numbers.
How is this different from just using a square or cube root calculator?
This generalizes to any root degree you choose, so instead of being limited to n=2 or n=3, you can find the 4th root, 7th root, or any other degree in one place.