The nth root of a number is the value that, raised to the power n, gives that number — written ⁿ√x or x^(1/n). It's the inverse of an nth power. Positive numbers always have a real root; negatives have a real root only for odd n, keeping the sign (³√(−27) = −3).
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the identity ⁿ√x = x^(1/n), recomputed in code.
What an nth root is
Finding ⁿ√x asks "what number to the power n gives x?" Computing x^(1/n) answers it. For a positive x the result is real for any n. For a negative x, even powers can't be negative, so only an odd n yields a real (negative) root; even roots of negatives are complex. Fractional exponents generalise this: x^(m/n) is the nth root of x to the mth power.
Worked examples
The 4th root of 16:
The 5th root of 100:
An odd root of a negative, ³√(−27):
So ⁴√16 is exactly 2, ⁵√100 is the irrational 2.5119…, and ³√(−27) is −3. By contrast ⁴√(−16) has no real value.
Frequently Asked Questions
ⁿ√x is the number that to the power n gives x. 2⁴ = 16, so ⁴√16 = 2. Same as x^(1/n).
Raise to 1/n: ⁵√32 = 32^(0.2) = 2; ⁵√100 ≈ 2.5119.
Real only for odd n. ³√(−27) = −3; ⁴√(−16) has no real value.
Same thing. x^(1/n) is the nth root; x^(m/n) is the nth root to the mth power. 8^(2/3) = 4.
They're n = 2 and n = 3. The nth root generalises to any degree.