Cube Root of 63

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Cube root of

What is the cube root of 63?

Answer

∛63 ≈
3.9791

Real cube root: the only number whose cube is 63.

≈ — rounded to 4 decimal places. 63 is not the cube of a rational number, so ∛63 is irrational: its decimal expansion never ends and never repeats.

Prime factors
63 = 3 × 3 × 7 = 3² × 7
Take out of the root
No prime appears three times, so ∛63 is already in simplest form.
Between cubes
3³ = 27 < 63 < 64 = 4³, so 3 < ∛63 < 4 and ∛63 ≈ 3.9791

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
60≈ 3.9149
61≈ 3.9365
62≈ 3.9579
63≈ 3.9791
644
65≈ 4.0207
66≈ 4.0412

FAQ

What is the cube root of 63?

∛63 ≈ 3.9791

Can ∛63 be simplified?

No: no prime appears three times in 63, so its only cube factor is 1 and ∛63 is already in simplest form. Since 3³ = 27 < 63 < 64 = 4³, ∛63 lies between 3 and 4: ∛63 ≈ 3.9791.

Is ∛63 a rational number?

No: 63 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 ∛63 is irrational; its decimal never ends and never repeats: ∛63 ≈ 3.9791.

See Also