Cube Root of −4096

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What is the cube root of −4,096?

Answer

∛(−4,096) =
−16

Real cube root: the only number whose cube is −4,096.

A negative number has a negative cube root: (−16)³ = −4,096. There is no real square root of −4,096.

Sign
∛(−4,096) = −∛4,096, because (−a)³ = −a³
Prime factors
4,096 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 2¹²
Take out of the root
∛4,096 = ∛((2³)⁴) = 2⁴ = 16
Check
16 × 16 × 16 = 4,096 ✓

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−6,859−19
−5,832−18
−4,913−17
−4,096−16
−3,375−15
−2,744−14
−2,197−13

FAQ

What is the cube root of −4,096?

∛(−4,096) = −16

Why does the cube root of −4,096 exist but the square root does not?

A cube keeps the sign: (−16)³ = −4,096, so ∛(−4,096) = −16. The square of any real number is never negative, so no real number squared gives −4,096.

Is ∛(−4,096) a rational number?

Yes: ∛(−4,096) = −16, a whole number.

See Also