Cube Root of −1/8

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What is the cube root of −1/8?

Answer

∛(−1/8) =
−1/2 = −0.5

Real cube root: the only number whose cube is −1/8.

A negative number has a negative cube root: (−1/2)³ = −1/8. There is no real square root of −1/8.

Sign
∛(−1/8) = −∛(1/8), because (−a)³ = −a³
Root of a fraction
∛(1/8) = ∛1/∛8 = 1/2

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−1−1
−0.5≈ −0.7937
−1/2−∛4/2 ≈ −0.7937
−1/8−1/2 = −0.5
−0.0125≈ −0.2321
00
0.00015≈ 0.0531

FAQ

What is the cube root of −1/8?

∛(−1/8) = −1/2 = −0.5

Why does the cube root of −1/8 exist but the square root does not?

A cube keeps the sign: (−1/2)³ = −1/8, so ∛(−1/8) = −1/2. The square of any real number is never negative, so no real number squared gives −1/8.

Is ∛(−1/8) a rational number?

Yes: ∛(−1/8) = −1/2 = −0.5, a terminating decimal.

See Also