Cube Root of −6859

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Cube root of

What is the cube root of −6,859?

Answer

∛(−6,859) =
−19

Real cube root: the only number whose cube is −6,859.

A negative number has a negative cube root: (−19)³ = −6,859. There is no real square root of −6,859.

Sign
∛(−6,859) = −∛6,859, because (−a)³ = −a³
Prime factors
6,859 = (19 × 19 × 19) = 19³
Take out of the root
∛6,859 = ∛(19³) = 19
Check
19 × 19 × 19 = 6,859 ✓

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−106,875−5∛855 ≈ −47.4561
−8,000−20
−6,859−19
−5,832−18
−4,913−17
−4,096−16
−3,375−15

FAQ

What is the cube root of −6,859?

∛(−6,859) = −19

Why does the cube root of −6,859 exist but the square root does not?

A cube keeps the sign: (−19)³ = −6,859, so ∛(−6,859) = −19. The square of any real number is never negative, so no real number squared gives −6,859.

Is ∛(−6,859) a rational number?

Yes: ∛(−6,859) = −19, a whole number.

See Also