Is the cube root of a negative number really negative?

Yes — e.g. the cube root of −27 is −3, since (−3) × (−3) × (−3) = −27.

Yes — a negative n computes the reciprocal root (e.g. x^(1/−2) = 1 ÷ √x).

Math & Everyday

Root Calculator

Square root, cube root, or any nth root — including real roots of negative numbers.

🔒 Runs entirely in your browser — nothing here is ever uploaded

Computes the nth root of any number — square root, cube root, or any higher root — including real roots of negative numbers where one exists.

100% Free Runs in Your Browser No Sign-Up Required

How to use it

Formula

nth root of x = x^(1/n). For a negative x with an odd n, the real result is −(nth root of |x|).

Worked example

Cube root of −27 = −3, since (−3)³ = −27. 4th root of 16 = 2, since 2⁴ = 16.

Recommendations

• An odd-degree root (cube root, 5th root, etc.) of a negative number always has a real result.
• An even-degree root (square root, 4th root, etc.) of a negative number has no real result — only a complex one.

Frequently asked questions

There's no real number that, raised to an even power, gives a negative result — only a complex one, which this tool doesn't compute.