Cube Root of −15

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What is the cube root of −15?

Answer

∛(−15) =
−∛15 ≈ −2.4662

Real cube root: the only number whose cube is −15.

≈ — rounded to 4 decimal places. −15 is not the cube of a rational number, so ∛(−15) is irrational: its decimal expansion never ends and never repeats.

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

Sign
∛(−15) = −∛15, because (−a)³ = −a³
Prime factors
15 = 3 × 5
Take out of the root
No prime appears three times, so ∛15 is already in simplest form.
Between cubes
2³ = 8 < 15 < 27 = 3³, so 2 < ∛15 < 3 and ∛15 ≈ 2.4662

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−25−∛25 ≈ −2.924
−21−∛21 ≈ −2.7589
−20−∛20 ≈ −2.7144
−15−∛15 ≈ −2.4662
−8−2
−7−∛7 ≈ −1.9129
−5−∛5 ≈ −1.71

FAQ

What is the cube root of −15?

∛(−15) = −∛15 ≈ −2.4662

Why does the cube root of −15 exist but the square root does not?

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

Is ∛(−15) a rational number?

No: −15 is not the cube of a rational number, and the cube root of a fraction p/q in lowest terms is rational only when p and q are both cubes. So ∛(−15) is irrational; its decimal never ends and never repeats: ∛(−15) ≈ −2.4662.

See Also