Cube Root of −1

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Cube root of

What is the cube root of −1?

Answer

∛(−1) =
−1

Real cube root: the only number whose cube is −1.

A negative number has a negative cube root: (−1)³ = −1. There is no real square root of −1.

Sign
∛(−1) = −∛1, because (−a)³ = −a³
Check
1 × 1 × 1 = 1 ✓

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−5−∛5 ≈ −1.71
−3−∛3 ≈ −1.4422
−2−∛2 ≈ −1.2599
−1−1
−0.5≈ −0.7937
−1/2−∛4/2 ≈ −0.7937
−1/8−1/2 = −0.5

FAQ

What is the cube root of −1?

∛(−1) = −1

Why does the cube root of −1 exist but the square root does not?

A cube keeps the sign: (−1)³ = −1, so ∛(−1) = −1. The square of any real number is never negative, so no real number squared gives −1.

Is ∛(−1) a rational number?

Yes: ∛(−1) = −1, a whole number.

See Also