1. **State the problem:** Simplify the expression $$\sqrt[3]{250} + 3\sqrt[3]{54}$$. 2. **Recall the cube root properties:** The cube root of a product is the product of the cube roots: $$\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}$$. 3. **Factor inside the cube roots:** $$\sqrt[3]{250} = \sqrt[3]{125 \times 2}$$ $$\sqrt[3]{54} = \sqrt[3]{27 \times 2}$$ 4. **Extract perfect cubes:** $$\sqrt[3]{125 \times 2} = \sqrt[3]{125} \times \sqrt[3]{2} = 5\sqrt[3]{2}$$ $$\sqrt[3]{27 \times 2} = \sqrt[3]{27} \times \sqrt[3]{2} = 3\sqrt[3]{2}$$ 5. **Substitute back into the expression:** $$5\sqrt[3]{2} + 3 \times 3\sqrt[3]{2} = 5\sqrt[3]{2} + 9\sqrt[3]{2}$$ 6. **Combine like terms:** $$5\sqrt[3]{2} + 9\sqrt[3]{2} = (5 + 9)\sqrt[3]{2} = 14\sqrt[3]{2}$$ **Final answer:** $$14\sqrt[3]{2}$$