Nth Root Calculator

Calculate any root — square, cube, or nth — with decimal precision and exact form, for any index from 2 to 32.

Quick presets

Result
Click the value to copy
Exact form
x^(1/n) = —
Note: even roots of negative numbers are not real (the result is a complex number). Try an odd n, or enter a non-negative value.
Verification
Scientific

Formula

n√x = x1/n  — the nth root of x is the number that, raised to the nth power, gives back x.
What is an nth root?

The nth root of a number x is a value y such that yn = x. For example, the 4th root of 81 is 3, because 34 = 81.

Can I take a root of a negative number?

Yes, but only when the root index n is odd. The cube root of −27 is −3, because (−3)3 = −27. Even roots of negative numbers are complex and are not computed here.

How precise is the answer?

Results are computed with JavaScript double-precision floating point (about 15–16 significant digits). Very large or very small values switch automatically to scientific notation.

Why n = 2 to 32?

This range covers every practical case you will encounter in math, physics, finance and engineering. Roots higher than 32 return values extremely close to 1 and are rarely useful.

Copied

This tool computes the nth root of a number for any index n from 2 to 32. Pick a preset (square, cube, 4th, 5th, 10th, 32nd) or drag the slider to set n, then type the radicand x. The result appears as a decimal value and in exact form, along with the working line x^(1/n) and a verification step.

Examples: set n = 2 and x = 144 to get 12 (since 12 × 12 = 144). Set n = 3 and x = 27 to get 3 (since 3 × 3 × 3 = 27). Set n = 4 and x = 81 to get 3 (since 3^4 = 81). Negative radicands are handled for odd n — for instance the cube root of −27 is −3. Even roots of negative numbers return a clear note, because their result is complex and not real. Very large or very small outputs automatically switch to scientific notation.