1. **State the problem:** Simplify the expression $$\sqrt[3]{24} + \sqrt[3]{15} \times \sqrt[3]{25}$$. 2. **Recall the property of cube roots:** For any real numbers $a$ and $b$, $$\sqrt[3]{a} \times \sqrt[3]{b} = \sqrt[3]{a \times b}$$. 3. **Apply the property to the multiplication part:** $$\sqrt[3]{15} \times \sqrt[3]{25} = \sqrt[3]{15 \times 25} = \sqrt[3]{375}$$. 4. **Rewrite the expression:** $$\sqrt[3]{24} + \sqrt[3]{375}$$. 5. **Simplify each cube root if possible:** - Factor 24: $24 = 8 \times 3$, and since $8 = 2^3$, $$\sqrt[3]{24} = \sqrt[3]{8 \times 3} = \sqrt[3]{8} \times \sqrt[3]{3} = 2 \sqrt[3]{3}$$. - Factor 375: $375 = 125 \times 3$, and since $125 = 5^3$, $$\sqrt[3]{375} = \sqrt[3]{125 \times 3} = \sqrt[3]{125} \times \sqrt[3]{3} = 5 \sqrt[3]{3}$$. 6. **Combine like terms:** $$2 \sqrt[3]{3} + 5 \sqrt[3]{3} = (2 + 5) \sqrt[3]{3} = 7 \sqrt[3]{3}$$. **Final answer:** $$7 \sqrt[3]{3}$$