Cube Root of −54

Cube Root Calculator
Cube root of

What is the cube root of −54?

Answer

∛(−54) =
−3∛2 ≈ −3.7798

Real cube root: the only number whose cube is −54.

≈ — rounded to 4 decimal places. −54 is not the cube of a rational number, so ∛(−54) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−3∛2)³ = −54. There is no real square root of −54.

Sign
∛(−54) = −∛54, because (−a)³ = −a³
Prime factors
54 = 2 × (3 × 3 × 3) = 2 × 3³
Take out of the root
∛54 = ∛(3³ × 2) = 3∛2
Between cubes
3³ = 27 < 54 < 64 = 4³, so 3 < ∛54 < 4 and ∛54 ≈ 3.7798

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−108−3∛4 ≈ −4.7622
−81−3∛3 ≈ −4.3267
−64−4
−54−3∛2 ≈ −3.7798
−49−∛49 ≈ −3.6593
−32−2∛4 ≈ −3.1748
−27−3

FAQ

What is the cube root of −54?

∛(−54) = −3∛2 ≈ −3.7798

Why does the cube root of −54 exist but the square root does not?

A cube keeps the sign: (−3∛2)³ = −54, so ∛(−54) = −3∛2. The square of any real number is never negative, so no real number squared gives −54.

Is ∛(−54) a rational number?

No: −54 is not the cube of a rational number, and the cube root of a fraction p/q in lowest terms is rational only when p and q are both cubes. So ∛(−54) is irrational; its decimal never ends and never repeats: ∛(−54) ≈ −3.7798.

See Also