Cube Root of −49

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What is the cube root of −49?

Answer

∛(−49) =
−∛49 ≈ −3.6593

Real cube root: the only number whose cube is −49.

≈ — rounded to 4 decimal places. −49 is not the cube of a rational number, so ∛(−49) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−∛49)³ = −49. There is no real square root of −49.

Sign
∛(−49) = −∛49, because (−a)³ = −a³
Prime factors
49 = 7 × 7 = 7²
Take out of the root
No prime appears three times, so ∛49 is already in simplest form.
Between cubes
3³ = 27 < 49 < 64 = 4³, so 3 < ∛49 < 4 and ∛49 ≈ 3.6593

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−81−3∛3 ≈ −4.3267
−64−4
−54−3∛2 ≈ −3.7798
−49−∛49 ≈ −3.6593
−32−2∛4 ≈ −3.1748
−27−3
−25−∛25 ≈ −2.924

FAQ

What is the cube root of −49?

∛(−49) = −∛49 ≈ −3.6593

Why does the cube root of −49 exist but the square root does not?

A cube keeps the sign: (−∛49)³ = −49, so ∛(−49) = −∛49. The square of any real number is never negative, so no real number squared gives −49.

Is ∛(−49) a rational number?

No: −49 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 ∛(−49) is irrational; its decimal never ends and never repeats: ∛(−49) ≈ −3.6593.

See Also