Cube Root of 2.25

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Cube root of

What is the cube root of 2.25?

Answer

∛2.25 ≈
1.3104

Real cube root: the only number whose cube is 2.25.

≈ — rounded to 4 decimal places. 2.25 is not the cube of a rational number, so ∛2.25 is irrational: its decimal expansion never ends and never repeats.

Between cubes
1³ = 1 < 2.25 < 8 = 2³, so 1 < ∛2.25 < 2 and ∛2.25 ≈ 1.3104

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1.7281.2
2≈ 1.2599
2.1971.3
2.25≈ 1.3104
2.5≈ 1.3572
5/2∛20/2 ≈ 1.3572
2.7≈ 1.3925

FAQ

What is the cube root of 2.25?

∛2.25 ≈ 1.3104

How to find ∛2.25 without a calculator?

Bracket it between cubes: 1³ = 1 < 2.25 < 8 = 2³, so ∛2.25 lies between 1 and 2. Narrowing the bracket digit by digit gives ∛2.25 ≈ 1.3104; 2.25 is not the cube of a decimal, so the root never ends.

Is ∛2.25 a rational number?

No: 2.25 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 ∛2.25 is irrational; its decimal never ends and never repeats: ∛2.25 ≈ 1.3104.

See Also