Cube Root of −2744

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What is the cube root of −2,744?

Answer

∛(−2,744) =
−14

Real cube root: the only number whose cube is −2,744.

A negative number has a negative cube root: (−14)³ = −2,744. There is no real square root of −2,744.

Sign
∛(−2,744) = −∛2,744, because (−a)³ = −a³
Prime factors
2,744 = (2 × 2 × 2) × (7 × 7 × 7) = 2³ × 7³
Take out of the root
∛2,744 = ∛(2³ × 7³) = 2 × 7 = 14
Check
14 × 14 × 14 = 2,744 ✓

See Also

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Cube roots of nearby values

N∛N
−4,913−17
−4,096−16
−3,375−15
−2,744−14
−2,197−13
−1,728−12
−1,331−11

FAQ

What is the cube root of −2,744?

∛(−2,744) = −14

Why does the cube root of −2,744 exist but the square root does not?

A cube keeps the sign: (−14)³ = −2,744, so ∛(−2,744) = −14. The square of any real number is never negative, so no real number squared gives −2,744.

Is ∛(−2,744) a rational number?

Yes: ∛(−2,744) = −14, a whole number.

See Also