Cube Root of −4913

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What is the cube root of −4,913?

Answer

∛(−4,913) =
−17

Real cube root: the only number whose cube is −4,913.

A negative number has a negative cube root: (−17)³ = −4,913. There is no real square root of −4,913.

Sign
∛(−4,913) = −∛4,913, because (−a)³ = −a³
Prime factors
4,913 = (17 × 17 × 17) = 17³
Take out of the root
∛4,913 = ∛(17³) = 17
Check
17 × 17 × 17 = 4,913 ✓

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
−8,000−20
−6,859−19
−5,832−18
−4,913−17
−4,096−16
−3,375−15
−2,744−14

FAQ

What is the cube root of −4,913?

∛(−4,913) = −17

Why does the cube root of −4,913 exist but the square root does not?

A cube keeps the sign: (−17)³ = −4,913, so ∛(−4,913) = −17. The square of any real number is never negative, so no real number squared gives −4,913.

Is ∛(−4,913) a rational number?

Yes: ∛(−4,913) = −17, a whole number.

See Also