Cube Root of −20

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What is the cube root of −20?

Answer

∛(−20) =
−∛20 ≈ −2.7144

Real cube root: the only number whose cube is −20.

≈ — rounded to 4 decimal places. −20 is not the cube of a rational number, so ∛(−20) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−∛20)³ = −20. There is no real square root of −20.

Sign
∛(−20) = −∛20, because (−a)³ = −a³
Prime factors
20 = 2 × 2 × 5 = 2² × 5
Take out of the root
No prime appears three times, so ∛20 is already in simplest form.
Between cubes
2³ = 8 < 20 < 27 = 3³, so 2 < ∛20 < 3 and ∛20 ≈ 2.7144

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−27−3
−25−∛25 ≈ −2.924
−21−∛21 ≈ −2.7589
−20−∛20 ≈ −2.7144
−15−∛15 ≈ −2.4662
−8−2
−7−∛7 ≈ −1.9129

FAQ

What is the cube root of −20?

∛(−20) = −∛20 ≈ −2.7144

Why does the cube root of −20 exist but the square root does not?

A cube keeps the sign: (−∛20)³ = −20, so ∛(−20) = −∛20. The square of any real number is never negative, so no real number squared gives −20.

Is ∛(−20) a rational number?

No: −20 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 ∛(−20) is irrational; its decimal never ends and never repeats: ∛(−20) ≈ −2.7144.

See Also