1. **Simplify** $\sqrt{75} + \sqrt{48} + \sqrt{12} - \sqrt{108}$. 2. **State the problem:** Simplify the sum and difference of surds. 3. **Recall:** $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and simplify square roots by factoring out perfect squares. 4. Simplify each term: $$\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$$ $$\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$$ $$\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$$ $$\sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3}$$ 5. Substitute back: $$5\sqrt{3} + 4\sqrt{3} + 2\sqrt{3} - 6\sqrt{3}$$ 6. Combine like terms: $$ (5 + 4 + 2 - 6)\sqrt{3} = 5\sqrt{3}$$ **Final answer:** $5\sqrt{3}$