Cube Root of −27

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What is the cube root of −27?

Answer

∛(−27) =
−3

Real cube root: the only number whose cube is −27.

A negative number has a negative cube root: (−3)³ = −27. There is no real square root of −27.

Sign
∛(−27) = −∛27, because (−a)³ = −a³
Prime factors
27 = (3 × 3 × 3) = 3³
Take out of the root
∛27 = ∛(3³) = 3
Check
3 × 3 × 3 = 27 ✓

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−54−3∛2 ≈ −3.7798
−49−∛49 ≈ −3.6593
−32−2∛4 ≈ −3.1748
−27−3
−25−∛25 ≈ −2.924
−21−∛21 ≈ −2.7589
−20−∛20 ≈ −2.7144

FAQ

What is the cube root of −27?

∛(−27) = −3

Why does the cube root of −27 exist but the square root does not?

A cube keeps the sign: (−3)³ = −27, so ∛(−27) = −3. The square of any real number is never negative, so no real number squared gives −27.

Is ∛(−27) a rational number?

Yes: ∛(−27) = −3, a whole number.

See Also