Cube Root of −343

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Cube root of

What is the cube root of −343?

Answer

∛(−343) =
−7

Real cube root: the only number whose cube is −343.

A negative number has a negative cube root: (−7)³ = −343. There is no real square root of −343.

Sign
∛(−343) = −∛343, because (−a)³ = −a³
Prime factors
343 = (7 × 7 × 7) = 7³
Take out of the root
∛343 = ∛(7³) = 7
Check
7 × 7 × 7 = 343 ✓

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Cube roots of nearby values

N∛N
−1,000−10
−729−9
−512−8
−343−7
−216−6
−125−5
−108−3∛4 ≈ −4.7622

FAQ

What is the cube root of −343?

∛(−343) = −7

Why does the cube root of −343 exist but the square root does not?

A cube keeps the sign: (−7)³ = −343, so ∛(−343) = −7. The square of any real number is never negative, so no real number squared gives −343.

Is ∛(−343) a rational number?

Yes: ∛(−343) = −7, a whole number.

See Also