Cube Root of −8

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What is the cube root of −8?

Answer

∛(−8) =
−2

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

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

Sign
∛(−8) = −∛8, because (−a)³ = −a³
Prime factors
8 = (2 × 2 × 2) = 2³
Take out of the root
∛8 = ∛(2³) = 2
Check
2 × 2 × 2 = 8 ✓

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−21−∛21 ≈ −2.7589
−20−∛20 ≈ −2.7144
−15−∛15 ≈ −2.4662
−8−2
−7−∛7 ≈ −1.9129
−5−∛5 ≈ −1.71
−3−∛3 ≈ −1.4422

FAQ

What is the cube root of −8?

∛(−8) = −2

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

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

Is ∛(−8) a rational number?

Yes: ∛(−8) = −2, a whole number.

See Also