Cube Root of 196

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Cube root of

What is the cube root of 196?

Answer

∛196 ≈
5.8088

Real cube root: the only number whose cube is 196.

≈ — rounded to 4 decimal places. 196 is not the cube of a rational number, so ∛196 is irrational: its decimal expansion never ends and never repeats.

Prime factors
196 = 2 × 2 × 7 × 7 = 2² × 7²
Take out of the root
No prime appears three times, so ∛196 is already in simplest form.
Between cubes
5³ = 125 < 196 < 216 = 6³, so 5 < ∛196 < 6 and ∛196 ≈ 5.8088

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
187≈ 5.7185
1893∛7 ≈ 5.7388
1924∛3 ≈ 5.769
196≈ 5.8088
197≈ 5.8186
2002∛25 ≈ 5.848
201≈ 5.8578

FAQ

What is the cube root of 196?

∛196 ≈ 5.8088

Can ∛196 be simplified?

No: no prime appears three times in 196, so its only cube factor is 1 and ∛196 is already in simplest form. Since 5³ = 125 < 196 < 216 = 6³, ∛196 lies between 5 and 6: ∛196 ≈ 5.8088.

Is ∛196 a rational number?

No: 196 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 ∛196 is irrational; its decimal never ends and never repeats: ∛196 ≈ 5.8088.

See Also