Cube Root of −0.5

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What is the cube root of −0.5?

Answer

∛(−0.5) ≈
−0.7937

Real cube root: the only number whose cube is −0.5.

≈ — rounded to 4 decimal places. −0.5 is not the cube of a rational number, so ∛(−0.5) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−a)³ = −a³, so ∛(−0.5) = −∛0.5. There is no real square root of −0.5.

−0.5 = −1/2.

Between cubes
0.7³ = 0.343 < 0.5 < 0.512 = 0.8³, so 0.7 < ∛0.5 < 0.8 and ∛0.5 ≈ 0.7937

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−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
−0.0125≈ −0.2321

FAQ

What is the cube root of −0.5?

∛(−0.5) ≈ −0.7937

Why does the cube root of −0.5 exist but the square root does not?

A cube keeps the sign: (−a)³ = −a³, so ∛(−0.5) = −∛0.5 ≈ −0.7937. The square of any real number is never negative, so no real number squared gives −0.5.

Is ∛(−0.5) a rational number?

No: −0.5 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 ∛(−0.5) is irrational; its decimal never ends and never repeats: ∛(−0.5) ≈ −0.7937.

See Also