To simplify numerical square, cube, and fourth roots, identify the largest perfect power factor that matches the root's index and apply the Product Property of Roots. For the square root $\sqrt{288}$, the largest perfect square factor is $144$, so rewrite it as $\sqrt{144 \cdot 2}$ and simplify to $12\sqrt{2}$. For the cube root $\sqrt[3]{81}$, the largest perfect cube factor is $27$ (since $3^3 = 27$), yielding $\sqrt[3]{27 \cdot 3}$, which simplifies to $3\sqrt[3]{3}$. For the fourth root $\sqrt[4]{64}$, the largest perfect fourth power factor is $16$ (since $2^4 = 16$), so rewrite it as $\sqrt[4]{16 \cdot 4}$ and simplify to $2\sqrt[4]{4}$.