Cube Root of −125

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Cube root of

What is the cube root of −125?

Answer

∛(−125) =
−5

Real cube root: the only number whose cube is −125.

A negative number has a negative cube root: (−5)³ = −125. There is no real square root of −125.

Sign
∛(−125) = −∛125, because (−a)³ = −a³
Prime factors
125 = (5 × 5 × 5) = 5³
Take out of the root
∛125 = ∛(5³) = 5
Check
5 × 5 × 5 = 125 ✓

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
−512−8
−343−7
−216−6
−125−5
−108−3∛4 ≈ −4.7622
−81−3∛3 ≈ −4.3267
−64−4

FAQ

What is the cube root of −125?

∛(−125) = −5

Why does the cube root of −125 exist but the square root does not?

A cube keeps the sign: (−5)³ = −125, so ∛(−125) = −5. The square of any real number is never negative, so no real number squared gives −125.

Is ∛(−125) a rational number?

Yes: ∛(−125) = −5, a whole number.

See Also