Cube Root of −25

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What is the cube root of −25?

Answer

∛(−25) =
−∛25 ≈ −2.924

Real cube root: the only number whose cube is −25.

≈ — rounded to 4 decimal places. −25 is not the cube of a rational number, so ∛(−25) is irrational: its decimal expansion never ends and never repeats.

A negative number has a negative cube root: (−∛25)³ = −25. There is no real square root of −25.

Sign
∛(−25) = −∛25, because (−a)³ = −a³
Prime factors
25 = 5 × 5 = 5²
Take out of the root
No prime appears three times, so ∛25 is already in simplest form.
Between cubes
2³ = 8 < 25 < 27 = 3³, so 2 < ∛25 < 3 and ∛25 ≈ 2.924

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−49−∛49 ≈ −3.6593
−32−2∛4 ≈ −3.1748
−27−3
−25−∛25 ≈ −2.924
−21−∛21 ≈ −2.7589
−20−∛20 ≈ −2.7144
−15−∛15 ≈ −2.4662

FAQ

What is the cube root of −25?

∛(−25) = −∛25 ≈ −2.924

Why does the cube root of −25 exist but the square root does not?

A cube keeps the sign: (−∛25)³ = −25, so ∛(−25) = −∛25. The square of any real number is never negative, so no real number squared gives −25.

Is ∛(−25) a rational number?

No: −25 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 ∛(−25) is irrational; its decimal never ends and never repeats: ∛(−25) ≈ −2.924.

See Also