Softonic

Nth Root Calculator

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Enter a radicand x and a root degree n, the calculator returns the nth root, ⁿ√x = x^(1/n). It covers the square root (n = 2), cube root (n = 3) and any higher degree, and it correctly handles odd roots of negative numbers (for example ³√-8 = -2). When you ask for an even root of a negative number the result is not a real number, and the tool tells you so instead of returning a wrong value.

How to find an nth root

  1. 1

    Enter the radicand

    The number you want the root of: the value under the radical sign. Any real number, positive or negative.

  2. 2

    Enter the root degree

    The index n: 2 for a square root, 3 for a cube root, 5 for a fifth root, and so on.

  3. 3

    Read the result

    The tool computes x^(1/n) instantly. For an even root of a negative number it reports that no real root exists.

The formula

The nth root of a number is the value that, raised to the power n, gives back the original number. It is the inverse of exponentiation:

ⁿ√x = x^(1/n)     ⟺     (ⁿ√x)^n = x

The number under the radical (x) is the radicand; the small index (n) is the degree or order of the root. A degree of 2 is the familiar square root (√x), a degree of 3 is the cube root (³√x), and any higher integer gives the corresponding higher-order root.

A worked example

To find the fourth root of 81, set x = 81 and n = 4:

⁴√81 = 81^(1/4) = (3⁴)^(1/4) = 3

You can verify it by squaring twice: 3 × 3 = 9, and 9 × 9 = 81. ✓

Common roots at a glance

Expression Degree n Result Check
√16 2 4 4² = 16
³√27 3 3 3³ = 27
³√-8 3 -2 (-2)³ = -8
⁴√81 4 3 3⁴ = 81
⁵√32 5 2 2⁵ = 32
³√2 3 ≈ 1.2599 1.2599³ ≈ 2

Pitfalls to watch for

  • Even roots of negatives have no real value. √-4 or ⁴√-16 are not real numbers; they live in the complex plane (√-4 = 2·i). This tool reports them as “not a real number” rather than guessing.
  • Odd roots of negatives are fine. Because (-2)³ = -8, the cube root ³√-8 = -2 is a perfectly valid real number, and the calculator returns it.
  • Degree 0 is undefined. x^(1/0) divides by zero, so a root of degree 0 has no meaning.
  • Many results are irrational. ³√2 and √2 never terminate or repeat; the displayed value is rounded to a fixed number of decimals.

Every calculation runs locally in your browser, the radicand and degree you type never leave the page.

Frequently Asked Questions

The nth root of x is the number that, raised to the power n, equals x. It is written ⁿ√x and is the same as x^(1/n). For example, the cube root of 27 is 3 because 3³ = 27.

Only for odd degrees. ³√-8 = -2 and ⁵√-32 = -2 are real numbers. Even roots of negatives (such as √-4) are not real, they are complex, so the calculator flags them instead of returning a value.

A square root calculator is fixed at degree 2. This tool lets you choose any degree n, so it computes square roots, cube roots, fourth roots, fifth roots and beyond from one place.

A root of degree 0 is undefined, because x^(1/0) would require dividing by zero. The calculator does not return a value for degree 0.

No. The calculation runs entirely in your browser, so neither the radicand nor the degree you enter ever leaves the page.

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