Cube Root of −3375

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What is the cube root of −3,375?

Answer

∛(−3,375) =
−15

Real cube root: the only number whose cube is −3,375.

A negative number has a negative cube root: (−15)³ = −3,375. There is no real square root of −3,375.

Sign
∛(−3,375) = −∛3,375, because (−a)³ = −a³
Prime factors
3,375 = (3 × 3 × 3) × (5 × 5 × 5) = 3³ × 5³
Take out of the root
∛3,375 = ∛(3³ × 5³) = 3 × 5 = 15
Check
15 × 15 × 15 = 3,375 ✓

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FAQ

What is the cube root of −3,375?

∛(−3,375) = −15

Why does the cube root of −3,375 exist but the square root does not?

A cube keeps the sign: (−15)³ = −3,375, so ∛(−3,375) = −15. The square of any real number is never negative, so no real number squared gives −3,375.

Is ∛(−3,375) a rational number?

Yes: ∛(−3,375) = −15, a whole number.

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