Cube Root of 448

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Cube root of

What is the cube root of 448?

Answer

∛448 =
4∛7 ≈ 7.6517

Real cube root: the only number whose cube is 448.

≈ — rounded to 4 decimal places. 448 is not the cube of a rational number, so ∛448 is irrational: its decimal expansion never ends and never repeats.

Prime factors
448 = (2 × 2 × 2) × (2 × 2 × 2) × 7 = 2⁶ × 7
Take out of the root
∛448 = ∛((2³)² × 7) = 2² × ∛7 = 4∛7
Between cubes
7³ = 343 < 448 < 512 = 8³, so 7 < ∛448 < 8 and ∛448 ≈ 7.6517

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
425≈ 7.5185
4326∛2 ≈ 7.5595
445≈ 7.6346
4484∛7 ≈ 7.6517
450≈ 7.6631
458≈ 7.7082
474.5527.8

FAQ

What is the cube root of 448?

∛448 = 4∛7 ≈ 7.6517

How to simplify ∛448?

Factor 448 into primes: 448 = 2 × 2 × 2 × 2 × 2 × 2 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛448 = ∛((2³)² × 7) = 4∛7.

Is ∛448 a rational number?

No: 448 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 ∛448 is irrational; its decimal never ends and never repeats: ∛448 ≈ 7.6517.

See Also