Cube Root of −2197

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What is the cube root of −2,197?

Answer

∛(−2,197) =
−13

Real cube root: the only number whose cube is −2,197.

A negative number has a negative cube root: (−13)³ = −2,197. There is no real square root of −2,197.

Sign
∛(−2,197) = −∛2,197, because (−a)³ = −a³
Prime factors
2,197 = (13 × 13 × 13) = 13³
Take out of the root
∛2,197 = ∛(13³) = 13
Check
13 × 13 × 13 = 2,197 ✓

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−4,096−16
−3,375−15
−2,744−14
−2,197−13
−1,728−12
−1,331−11
−1,000−10

FAQ

What is the cube root of −2,197?

∛(−2,197) = −13

Why does the cube root of −2,197 exist but the square root does not?

A cube keeps the sign: (−13)³ = −2,197, so ∛(−2,197) = −13. The square of any real number is never negative, so no real number squared gives −2,197.

Is ∛(−2,197) a rational number?

Yes: ∛(−2,197) = −13, a whole number.

See Also