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What is the cube root of 1,536?

Answer

∛1,536 =
8∛3 ≈ 11.538

Real cube root: the only number whose cube is 1,536.

≈ — rounded to 4 decimal places. 1,536 is not the cube of a rational number, so ∛1,536 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3 = 2⁹ × 3
Take out of the root
∛1,536 = ∛((2³)³ × 3) = 2³ × ∛3 = 8∛3
Between cubes
11³ = 1,331 < 1,536 < 1,728 = 12³, so 11 < ∛1,536 < 12 and ∛1,536 ≈ 11.538

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,4589∛2 ≈ 11.3393
1,4882∛186 ≈ 11.4165
1,521≈ 11.5003
1,5368∛3 ≈ 11.538
1,700≈ 11.9348
1,7013∛63 ≈ 11.9372
1,7157∛5 ≈ 11.9698

FAQ

What is the cube root of 1,536?

∛1,536 = 8∛3 ≈ 11.538

How to simplify ∛1,536?

Factor 1,536 into primes: 1,536 = 2 × 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: ∛1,536 = ∛((2³)³ × 3) = 8∛3.

Is ∛1,536 a rational number?

No: 1,536 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 ∛1,536 is irrational; its decimal never ends and never repeats: ∛1,536 ≈ 11.538.

See Also