Cube Root of 84

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Cube root of

What is the cube root of 84?

Answer

∛84 ≈
4.3795

Real cube root: the only number whose cube is 84.

≈ — rounded to 4 decimal places. 84 is not the cube of a rational number, so ∛84 is irrational: its decimal expansion never ends and never repeats.

Prime factors
84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
Take out of the root
No prime appears three times, so ∛84 is already in simplest form.
Between cubes
4³ = 64 < 84 < 125 = 5³, so 4 < ∛84 < 5 and ∛84 ≈ 4.3795

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
813∛3 ≈ 4.3267
82≈ 4.3445
83≈ 4.3621
84≈ 4.3795
85≈ 4.3968
86≈ 4.414
87≈ 4.431

FAQ

What is the cube root of 84?

∛84 ≈ 4.3795

Can ∛84 be simplified?

No: no prime appears three times in 84, so its only cube factor is 1 and ∛84 is already in simplest form. Since 4³ = 64 < 84 < 125 = 5³, ∛84 lies between 4 and 5: ∛84 ≈ 4.3795.

Is ∛84 a rational number?

No: 84 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 ∛84 is irrational; its decimal never ends and never repeats: ∛84 ≈ 4.3795.

See Also