Cube Root of −0.0125

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What is the cube root of −0.0125?

Answer

∛(−0.0125) ≈
−0.2321

Real cube root: the only number whose cube is −0.0125.

≈ — rounded to 4 decimal places. −0.0125 is not the cube of a rational number, so ∛(−0.0125) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−a)³ = −a³, so ∛(−0.0125) = −∛0.0125. There is no real square root of −0.0125.

Between cubes
0.2³ = 0.008 < 0.0125 < 0.027 = 0.3³, so 0.2 < ∛0.0125 < 0.3 and ∛0.0125 ≈ 0.2321

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−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
0.0008≈ 0.0928

FAQ

What is the cube root of −0.0125?

∛(−0.0125) ≈ −0.2321

Why does the cube root of −0.0125 exist but the square root does not?

A cube keeps the sign: (−a)³ = −a³, so ∛(−0.0125) = −∛0.0125 ≈ −0.2321. The square of any real number is never negative, so no real number squared gives −0.0125.

Is ∛(−0.0125) a rational number?

No: −0.0125 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 ∛(−0.0125) is irrational; its decimal never ends and never repeats: ∛(−0.0125) ≈ −0.2321.

See Also