Cube Root of 375

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Cube root of

What is the cube root of 375?

Answer

∛375 =
5∛3 ≈ 7.2112

Real cube root: the only number whose cube is 375.

≈ — rounded to 4 decimal places. 375 is not the cube of a rational number, so ∛375 is irrational: its decimal expansion never ends and never repeats.

Prime factors
375 = 3 × (5 × 5 × 5) = 3 × 5³
Take out of the root
∛375 = ∛(5³ × 3) = 5∛3
Between cubes
7³ = 343 < 375 < 512 = 8³, so 7 < ∛375 < 8 and ∛375 ≈ 7.2112

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Cube roots of nearby values

N∛N
331≈ 6.9174
3362∛42 ≈ 6.9521
3437
3755∛3 ≈ 7.2112
425≈ 7.5185
4326∛2 ≈ 7.5595
445≈ 7.6346

FAQ

What is the cube root of 375?

∛375 = 5∛3 ≈ 7.2112

How to simplify ∛375?

Factor 375 into primes: 375 = 3 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛375 = ∛(5³ × 3) = 5∛3.

Is ∛375 a rational number?

No: 375 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 ∛375 is irrational; its decimal never ends and never repeats: ∛375 ≈ 7.2112.

See Also