\( \leftarrow \)\begin{tabular}{l} Simplify. \\ \( \sqrt[3]{875} \) \\ \hline\end{tabular}

To simplify \( \sqrt[3]{875} \), we can first factor \( 875 \) into its prime factors. It breaks down into \( 875 = 5^3 \times 7 \). When taking the cube root, the cube of \( 5 \) comes out, leaving us with \( 5 \sqrt[3]{7} \). Therefore, \( \sqrt[3]{875} = 5\sqrt[3]{7} \) is the simplified form. For an interesting twist, did you know that cube roots like this can help when dealing with real-world problems? For instance, if you're looking to determine the volume of a cube that has a volume of \( 875 \) cubic units, calculating \( \sqrt[3]{875} \) gives you the length of one side, aiding in design or construction!