Cube Root of −7

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What is the cube root of −7?

Answer

∛(−7) =
−∛7 ≈ −1.9129

Real cube root: the only number whose cube is −7.

≈ — rounded to 4 decimal places. −7 is not the cube of a rational number, so ∛(−7) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−∛7)³ = −7. There is no real square root of −7.

Sign
∛(−7) = −∛7, because (−a)³ = −a³
Prime factors
7 is a prime number: no triple of equal factors.
Between cubes
1³ = 1 < 7 < 8 = 2³, so 1 < ∛7 < 2 and ∛7 ≈ 1.9129

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−20−∛20 ≈ −2.7144
−15−∛15 ≈ −2.4662
−8−2
−7−∛7 ≈ −1.9129
−5−∛5 ≈ −1.71
−3−∛3 ≈ −1.4422
−2−∛2 ≈ −1.2599

FAQ

What is the cube root of −7?

∛(−7) = −∛7 ≈ −1.9129

Why does the cube root of −7 exist but the square root does not?

A cube keeps the sign: (−∛7)³ = −7, so ∛(−7) = −∛7. The square of any real number is never negative, so no real number squared gives −7.

Is ∛(−7) a rational number?

No: −7 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 ∛(−7) is irrational; its decimal never ends and never repeats: ∛(−7) ≈ −1.9129.

See Also