Nth Root Calculator
The nth root of a number x is the value that, when multiplied by itself n times, equals x. This calculator computes the nth root for any positive root degree n, including decimal degrees. For example, the 4th root of 16 is 2 (since 2^4 = 16), and the cube root of 8 is 2 (since 2^3 = 8). The calculator displays the result in decimal form and shows the equivalent exponential form. For instance, the nth root of x is equivalent to x^(1/n). Roots are fundamental in algebra, geometry, and science. They are used in solving polynomial equations, calculating dimensions from volumes, and understanding scaling relationships. The nth root generalizes the square root (n=2) and cube root (n=3) to any positive integer or decimal degree.
Nth root formula
ⁿ√x = x^(1/n)
The nth root of x is the value a such that a^n = x
Can also be written as: ⁿ√x = x^(1/n)
For fractional roots: x^(m/n) = (ⁿ√x)^m
Common roots
| Number | Square root (n=2) | Cube root (n=3) | 4th root (n=4) |
|---|---|---|---|
| 1 | 1.00 | 1.00 | 1.00 |
| 2 | 1.41 | 1.26 | 1.19 |
| 4 | 2.00 | 1.59 | 1.41 |
| 8 | 2.83 | 2.00 | 1.68 |
| 16 | 4.00 | 2.52 | 2.00 |
| 27 | 5.20 | 3.00 | 2.28 |
| 32 | 5.66 | 3.17 | 2.38 |
| 64 | 8.00 | 4.00 | 2.83 |
| 100 | 10.00 | 4.64 | 3.16 |
| 1000 | 31.62 | 10.00 | 5.62 |
Nth root calculator: frequently asked questions
What is an nth root?
The nth root of a number x is the value that, when multiplied by itself n times, equals x. For example, the 4th root of 16 is 2, because 2 × 2 × 2 × 2 = 16. The nth root is written as cbrt(x) or x^(1/n).
What is the difference between a square root, cube root, and nth root?
A square root is the 2nd root (n=2). A cube root is the 3rd root (n=3). An nth root generalizes this to any positive integer n. sqrt(x) = x^(1/2), cbrt(x) = x^(1/3), and the nth root of x is x^(1/n).
Can you take an even root of a negative number?
No, you cannot take an even root (2nd, 4th, 6th, etc.) of a negative number in the real number system. However, you can take odd roots (3rd, 5th, 7th, etc.) of negative numbers. For example, the 3rd root of -8 is -2.
What is x^(1/n)?
x^(1/n) is the nth root of x. This is the exponential notation for roots. For example, x^(1/2) is the square root of x, and x^(1/3) is the cube root of x.
How do fractional exponents work?
A fractional exponent a^(m/n) means to take the nth root and then raise to the m power: a^(m/n) = (a^(1/n))^m. For example, 8^(2/3) = (8^(1/3))^2 = 2^2 = 4.
Official sources
- Roots and exponents: NIST Special Publication 330.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.