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What is the cube root of 1,521?

Answer

∛1,521 ≈
11.5003

Real cube root: the only number whose cube is 1,521.

≈ — rounded to 4 decimal places. 1,521 is not the cube of a rational number, so ∛1,521 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,521 = 3 × 3 × 13 × 13 = 3² × 13²
Take out of the root
No prime appears three times, so ∛1,521 is already in simplest form.
Between cubes
11³ = 1,331 < 1,521 < 1,728 = 12³, so 11 < ∛1,521 < 12 and ∛1,521 ≈ 11.5003

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,3727∛4 ≈ 11.1118
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

FAQ

What is the cube root of 1,521?

∛1,521 ≈ 11.5003

Can ∛1,521 be simplified?

No: no prime appears three times in 1,521, so its only cube factor is 1 and ∛1,521 is already in simplest form. Since 11³ = 1,331 < 1,521 < 1,728 = 12³, ∛1,521 lies between 11 and 12: ∛1,521 ≈ 11.5003.

Is ∛1,521 a rational number?

No: 1,521 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 ∛1,521 is irrational; its decimal never ends and never repeats: ∛1,521 ≈ 11.5003.

See Also