Explain why f(x) = ∛x has domain all real numbers while f(x) = √x does not. Which mathematical property accounts for this difference?

Odd roots (such as cube roots) produce a real value for every real input, including negatives, whereas even roots require nonnegative radicands to yield real outputs.

Cube roots are periodic functions, so their domain includes all real numbers, unlike square roots.

Cube roots are polynomials and therefore accept all real inputs, while square roots are not polynomials and restrict inputs.

Cube roots are defined only for integers, allowing negative values, whereas square roots are not.