1. **State the problem:** Simplify the expression $$\sqrt{75} - \sqrt{3} + \sqrt{8}$$ to its simplest radical form. 2. **Recall the rule:** To simplify square roots, factor the number inside the root into a product of a perfect square and another number, then use $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. 3. **Simplify each term:** - $$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$$ - $$\sqrt{3}$$ stays as is. - $$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$$ 4. **Rewrite the expression:** $$5\sqrt{3} - \sqrt{3} + 2\sqrt{2}$$ 5. **Combine like terms:** $$5\sqrt{3} - \sqrt{3} = (5 - 1)\sqrt{3} = 4\sqrt{3}$$ 6. **Final simplified expression:** $$4\sqrt{3} + 2\sqrt{2}$$ This is the simplest radical form because $$\sqrt{3}$$ and $$\sqrt{2}$$ are unlike terms and cannot be combined further.