The cube root of a number is the value that, multiplied by itself three times, gives that number — written ∛x or x^(1/3). It undoes cubing. Because a negative cubed stays negative, cube roots of negatives are real: ∛(−8) = −2. A perfect cube like 27 or 125 has a whole-number root.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the cube-root definition (y³ = x), recomputed in code.
What a cube root is
Finding ∛x means asking "what number cubed gives x?" For perfect cubes the answer is a whole number — ∛27 = 3 because 3 × 3 × 3 = 27. For everything else it's an irrational decimal. The sign carries through: a negative input gives a negative root, since three negatives multiply to a negative.
Worked examples
A perfect cube, 64:
A negative, −8:
A non-perfect cube, 10:
So 64 and −8 have the clean roots 4 and −2, while 10 gives the irrational 2.1544…. The calculator flags which inputs are perfect cubes.
Frequently Asked Questions
∛x is the number that cubes to x. 4³ = 64, so ∛64 = 4. Same as x^(1/3).
Real and negative: (−2)³ = −8 so ∛(−8) = −2. Cube roots keep the sign.
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 — cubes of 1–10. Whole-number roots.
≈ 2.1544 — irrational, since 10 isn't a perfect cube.
Cube undoes power 3 and works for negatives; square undoes power 2 and isn't real for negatives.