Cube Root of −216

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What is the cube root of −216?

Answer

∛(−216) =
−6

Real cube root: the only number whose cube is −216.

A negative number has a negative cube root: (−6)³ = −216. There is no real square root of −216.

Sign
∛(−216) = −∛216, because (−a)³ = −a³
Prime factors
216 = (2 × 2 × 2) × (3 × 3 × 3) = 2³ × 3³
Take out of the root
∛216 = ∛(2³ × 3³) = 2 × 3 = 6
Check
6 × 6 × 6 = 216 ✓

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Cube roots of nearby values

N∛N
−729−9
−512−8
−343−7
−216−6
−125−5
−108−3∛4 ≈ −4.7622
−81−3∛3 ≈ −4.3267

FAQ

What is the cube root of −216?

∛(−216) = −6

Why does the cube root of −216 exist but the square root does not?

A cube keeps the sign: (−6)³ = −216, so ∛(−216) = −6. The square of any real number is never negative, so no real number squared gives −216.

Is ∛(−216) a rational number?

Yes: ∛(−216) = −6, a whole number.

See Also