Work out cube root by hand instantly with clear inputs, formula shown and shareable results.
Newton's method applied to x³ − v = 0 gives the iteration x ← x − (x³ − v)/(3x²). Unlike square roots, cube roots exist for negative numbers, so the sign is carried through.
Newton iteration
xₖ₊₁ = xₖ − (xₖ³ − v) / (3xₖ²)
Exactly 17, since 17³ = 4913.
Yes. ∛(−27) = −3, because a negative cubed is negative.