Cube Root of 1225

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What is the cube root of 1,225?

Answer

∛1,225 ≈
10.6999

Real cube root: the only number whose cube is 1,225.

≈ — rounded to 4 decimal places. 1,225 is not the cube of a rational number, so ∛1,225 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,225 = 5 × 5 × 7 × 7 = 5² × 7²
Take out of the root
No prime appears three times, so ∛1,225 is already in simplest form.
Between cubes
10³ = 1,000 < 1,225 < 1,331 = 11³, so 10 < ∛1,225 < 11 and ∛1,225 ≈ 10.6999

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,1255∛9 ≈ 10.4004
1,2002∛150 ≈ 10.6266
1,210≈ 10.656
1,225≈ 10.6999
1,2804∛20 ≈ 10.8577
1,2966∛6 ≈ 10.9027
1,3233∛49 ≈ 10.9779

FAQ

What is the cube root of 1,225?

∛1,225 ≈ 10.6999

Can ∛1,225 be simplified?

No: no prime appears three times in 1,225, so its only cube factor is 1 and ∛1,225 is already in simplest form. Since 10³ = 1,000 < 1,225 < 1,331 = 11³, ∛1,225 lies between 10 and 11: ∛1,225 ≈ 10.6999.

Is ∛1,225 a rational number?

No: 1,225 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 ∛1,225 is irrational; its decimal never ends and never repeats: ∛1,225 ≈ 10.6999.

See Also