Cube Root of −3

Cube Root Calculator
Cube root of

What is the cube root of −3?

Answer

∛(−3) =
−∛3 ≈ −1.4422

Real cube root: the only number whose cube is −3.

≈ — rounded to 4 decimal places. −3 is not the cube of a rational number, so ∛(−3) is irrational: its decimal expansion never ends and never repeats.

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

Sign
∛(−3) = −∛3, because (−a)³ = −a³
Prime factors
3 is a prime number: no triple of equal factors.
Between cubes
1³ = 1 < 3 < 8 = 2³, so 1 < ∛3 < 2 and ∛3 ≈ 1.4422

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−8−2
−7−∛7 ≈ −1.9129
−5−∛5 ≈ −1.71
−3−∛3 ≈ −1.4422
−2−∛2 ≈ −1.2599
−1−1
−0.5≈ −0.7937

FAQ

What is the cube root of −3?

∛(−3) = −∛3 ≈ −1.4422

Why does the cube root of −3 exist but the square root does not?

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

Is ∛(−3) a rational number?

No: −3 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 ∛(−3) is irrational; its decimal never ends and never repeats: ∛(−3) ≈ −1.4422.

See Also