1. **State the problem:** Simplify the expression $$\sqrt[3]{50} - \sqrt{18} + \sqrt{98}$$. 2. **Recall the rules:** - Cube root: $$\sqrt[3]{a} = a^{1/3}$$. - Square root: $$\sqrt{a} = a^{1/2}$$. - Simplify roots by factoring out perfect powers. 3. **Simplify each term:** - $$\sqrt[3]{50} = \sqrt[3]{25 \times 2} = \sqrt[3]{5^2 \times 2}$$ (no perfect cube factors, so keep as is). - $$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$$. - $$\sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \times \sqrt{2} = 7\sqrt{2}$$. 4. **Rewrite the expression:** $$\sqrt[3]{50} - 3\sqrt{2} + 7\sqrt{2}$$. 5. **Combine like terms:** $$-3\sqrt{2} + 7\sqrt{2} = (7 - 3)\sqrt{2} = 4\sqrt{2}$$. 6. **Final simplified expression:** $$\sqrt[3]{50} + 4\sqrt{2}$$. This is the simplest form since $$\sqrt[3]{50}$$ cannot be simplified further.