Cube Root of 72

Cube Root Calculator
Cube root of

What is the cube root of 72?

Answer

∛72 =
2∛9 ≈ 4.1602

Real cube root: the only number whose cube is 72.

≈ — rounded to 4 decimal places. 72 is not the cube of a rational number, so ∛72 is irrational: its decimal expansion never ends and never repeats.

Prime factors
72 = (2 × 2 × 2) × 3 × 3 = 2³ × 3²
Take out of the root
∛72 = ∛(2³ × 9) = 2∛9
Between cubes
4³ = 64 < 72 < 125 = 5³, so 4 < ∛72 < 5 and ∛72 ≈ 4.1602

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
69≈ 4.1016
70≈ 4.1213
71≈ 4.1408
722∛9 ≈ 4.1602
73≈ 4.1793
74≈ 4.1983
75≈ 4.2172

FAQ

What is the cube root of 72?

∛72 = 2∛9 ≈ 4.1602

How to simplify ∛72?

Factor 72 into primes: 72 = 2 × 2 × 2 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛72 = ∛(2³ × 9) = 2∛9.

Is ∛72 a rational number?

No: 72 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 ∛72 is irrational; its decimal never ends and never repeats: ∛72 ≈ 4.1602.

See Also