Cube Root of −1728

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What is the cube root of −1,728?

Answer

∛(−1,728) =
−12

Real cube root: the only number whose cube is −1,728.

A negative number has a negative cube root: (−12)³ = −1,728. There is no real square root of −1,728.

Sign
∛(−1,728) = −∛1,728, because (−a)³ = −a³
Prime factors
1,728 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) = 2⁶ × 3³
Take out of the root
∛1,728 = ∛((2³)² × 3³) = 2² × 3 = 12
Check
12 × 12 × 12 = 1,728 ✓

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−3,375−15
−2,744−14
−2,197−13
−1,728−12
−1,331−11
−1,000−10
−729−9

FAQ

What is the cube root of −1,728?

∛(−1,728) = −12

Why does the cube root of −1,728 exist but the square root does not?

A cube keeps the sign: (−12)³ = −1,728, so ∛(−1,728) = −12. The square of any real number is never negative, so no real number squared gives −1,728.

Is ∛(−1,728) a rational number?

Yes: ∛(−1,728) = −12, a whole number.

See Also