Nth Root Calculator
Calculate the nth root of any number (square root, cube root, etc.).
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How to use this tool
- Enter number and root (n) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your result and the full breakdown beneath it.
Calculate the nth root of any positive number. The 2nd root is the square root; the 3rd root is the cube root.
Formula
ⁿ√x = x1/n
Computed as Math.pow(x, 1/n), which raises x to the reciprocal of n.
How it works
The calculator raises the input number x to the power of 1/n using the standard power identity, which is equivalent to taking the nth root. This works for any positive x and positive real n; results for negative x or non-integer n may be NaN or complex (not supported).
Worked example
Worked example: cube root of 27
- Input: x = 27, n = 3.
- Apply the formula: 271/3.
- Compute: 271/3 = 3, because 3 × 3 × 3 = 27.
The cube root of 27 is 3
Common mistakes to avoid
- Taking an even root of a negative number -- real even-index roots of negative numbers are undefined; the calculator will return NaN, which is correct but surprises users expecting a numeric answer.
- Confusing the nth root with dividing by n -- the cube root of 27 is 3 (because 3^3 = 27), not 9 (27 divided by 3).
- Entering n = 0 as the root degree -- raising a number to the power 1/0 is undefined; this is effectively a division-by-zero error in the exponent.
Key terms
- Nth root
- A value r such that r raised to the power n equals the original number x.
- Radicand
- The number under a root sign; here, the value x whose root is being found.
- Index (n)
- The degree of the root — 2 for square root, 3 for cube root, etc.
- Power identity
- The rule that ⁿ√x = x^(1/n), allowing roots to be computed via exponentiation.
Frequently asked questions
- How do you calculate the nth root?
- The nth root of x equals x raised to the power of 1/n. For example, the cube root of 27 is 27^(1/3) = 3.