Cube Root of −2

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What is the cube root of −2?

Answer

∛(−2) =
−∛2 ≈ −1.2599

Real cube root: the only number whose cube is −2.

≈ — rounded to 4 decimal places. −2 is not the cube of a rational number, so ∛(−2) is irrational: its decimal expansion never ends and never repeats.

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

Sign
∛(−2) = −∛2, because (−a)³ = −a³
Prime factors
2 is a prime number: no triple of equal factors.
Between cubes
1³ = 1 < 2 < 8 = 2³, so 1 < ∛2 < 2 and ∛2 ≈ 1.2599

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−7−∛7 ≈ −1.9129
−5−∛5 ≈ −1.71
−3−∛3 ≈ −1.4422
−2−∛2 ≈ −1.2599
−1−1
−0.5≈ −0.7937
−1/2−∛4/2 ≈ −0.7937

FAQ

What is the cube root of −2?

∛(−2) = −∛2 ≈ −1.2599

Why does the cube root of −2 exist but the square root does not?

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

Is ∛(−2) a rational number?

No: −2 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 ∛(−2) is irrational; its decimal never ends and never repeats: ∛(−2) ≈ −1.2599.

See Also