Cube Root of −1331

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What is the cube root of −1,331?

Answer

∛(−1,331) =
−11

Real cube root: the only number whose cube is −1,331.

A negative number has a negative cube root: (−11)³ = −1,331. There is no real square root of −1,331.

Sign
∛(−1,331) = −∛1,331, because (−a)³ = −a³
Prime factors
1,331 = (11 × 11 × 11) = 11³
Take out of the root
∛1,331 = ∛(11³) = 11
Check
11 × 11 × 11 = 1,331 ✓

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−2,744−14
−2,197−13
−1,728−12
−1,331−11
−1,000−10
−729−9
−512−8

FAQ

What is the cube root of −1,331?

∛(−1,331) = −11

Why does the cube root of −1,331 exist but the square root does not?

A cube keeps the sign: (−11)³ = −1,331, so ∛(−1,331) = −11. The square of any real number is never negative, so no real number squared gives −1,331.

Is ∛(−1,331) a rational number?

Yes: ∛(−1,331) = −11, a whole number.

See Also