Cube Root of 75

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Cube root of

What is the cube root of 75?

Answer

∛75 ≈
4.2172

Real cube root: the only number whose cube is 75.

≈ — rounded to 4 decimal places. 75 is not the cube of a rational number, so ∛75 is irrational: its decimal expansion never ends and never repeats.

Prime factors
75 = 3 × 5 × 5 = 3 × 5²
Take out of the root
No prime appears three times, so ∛75 is already in simplest form.
Between cubes
4³ = 64 < 75 < 125 = 5³, so 4 < ∛75 < 5 and ∛75 ≈ 4.2172

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
722∛9 ≈ 4.1602
73≈ 4.1793
74≈ 4.1983
75≈ 4.2172
76≈ 4.2358
77≈ 4.2543
78≈ 4.2727

FAQ

What is the cube root of 75?

∛75 ≈ 4.2172

Can ∛75 be simplified?

No: no prime appears three times in 75, so its only cube factor is 1 and ∛75 is already in simplest form. Since 4³ = 64 < 75 < 125 = 5³, ∛75 lies between 4 and 5: ∛75 ≈ 4.2172.

Is ∛75 a rational number?

No: 75 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 ∛75 is irrational; its decimal never ends and never repeats: ∛75 ≈ 4.2172.

See Also