Cube Root of −1/2

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What is the cube root of −1/2?

Answer

∛(−1/2) =
−∛4/2 ≈ −0.7937

Real cube root: the only number whose cube is −1/2.

≈ — rounded to 4 decimal places. −1/2 is not the cube of a rational number, so ∛(−1/2) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−∛4/2)³ = −1/2. There is no real square root of −1/2.

−1/2 = −0.5.

Sign
∛(−1/2) = −∛(1/2), because (−a)³ = −a³
Root of a fraction
∛(1/2) = ∛1/∛2 = 1/∛2
Multiply by ∛(2²) = ∛4
1/∛2 = ∛4/∛8 = ∛4/2 ≈ 0.7937

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−2−∛2 ≈ −1.2599
−1−1
−0.5≈ −0.7937
−1/2−∛4/2 ≈ −0.7937
−1/8−1/2 = −0.5
−0.0125≈ −0.2321
00

FAQ

What is the cube root of −1/2?

∛(−1/2) = −∛4/2 ≈ −0.7937

Why does the cube root of −1/2 exist but the square root does not?

A cube keeps the sign: (−∛4/2)³ = −1/2, so ∛(−1/2) = −∛4/2. The square of any real number is never negative, so no real number squared gives −1/2.

Is ∛(−1/2) a rational number?

No: −1/2 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 ∛(−1/2) is irrational; its decimal never ends and never repeats: ∛(−1/2) ≈ −0.7937.

See Also