Cube Root of −21

Cube Root Calculator
Cube root of

What is the cube root of −21?

Answer

∛(−21) =
−∛21 ≈ −2.7589

Real cube root: the only number whose cube is −21.

≈ — rounded to 4 decimal places. −21 is not the cube of a rational number, so ∛(−21) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−∛21)³ = −21. There is no real square root of −21.

Sign
∛(−21) = −∛21, because (−a)³ = −a³
Prime factors
21 = 3 × 7
Take out of the root
No prime appears three times, so ∛21 is already in simplest form.
Between cubes
2³ = 8 < 21 < 27 = 3³, so 2 < ∛21 < 3 and ∛21 ≈ 2.7589

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−32−2∛4 ≈ −3.1748
−27−3
−25−∛25 ≈ −2.924
−21−∛21 ≈ −2.7589
−20−∛20 ≈ −2.7144
−15−∛15 ≈ −2.4662
−8−2

FAQ

What is the cube root of −21?

∛(−21) = −∛21 ≈ −2.7589

Why does the cube root of −21 exist but the square root does not?

A cube keeps the sign: (−∛21)³ = −21, so ∛(−21) = −∛21. The square of any real number is never negative, so no real number squared gives −21.

Is ∛(−21) a rational number?

No: −21 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 ∛(−21) is irrational; its decimal never ends and never repeats: ∛(−21) ≈ −2.7589.

See Also