Cube Root of 768

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Cube root of

What is the cube root of 768?

Answer

∛768 =
4∛12 ≈ 9.1577

Real cube root: the only number whose cube is 768.

≈ — rounded to 4 decimal places. 768 is not the cube of a rational number, so ∛768 is irrational: its decimal expansion never ends and never repeats.

Prime factors
768 = (2 × 2 × 2) × (2 × 2 × 2) × 2 × 2 × 3 = 2⁸ × 3
Take out of the root
∛768 = ∛((2³)² × 12) = 2² × ∛12 = 4∛12
Between cubes
9³ = 729 < 768 < 1,000 = 10³, so 9 < ∛768 < 10 and ∛768 ≈ 9.1577

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
700≈ 8.879
7299
730≈ 9.0041
7684∛12 ≈ 9.1577
8646∛4 ≈ 9.5244
900≈ 9.6549
925≈ 9.7435

FAQ

What is the cube root of 768?

∛768 = 4∛12 ≈ 9.1577

How to simplify ∛768?

Factor 768 into primes: 768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛768 = ∛((2³)² × 12) = 4∛12.

Is ∛768 a rational number?

No: 768 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 ∛768 is irrational; its decimal never ends and never repeats: ∛768 ≈ 9.1577.

See Also