1. Simplify $\sqrt{75} + \sqrt{48} + \sqrt{12} - \sqrt{108}$. 2. Use the formula for squares of binomials: $(a - b)^2 = a^2 - 2ab + b^2$ and $(a + b)^2 = a^2 + 2ab + b^2$. 3. Simplify each surd by factoring out perfect squares. 4. Calculate each square root and simplify. Step 1: Simplify each surd. $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$ $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$ $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$ $\sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3}$ Step 2: Substitute back. $5\sqrt{3} + 4\sqrt{3} + 2\sqrt{3} - 6\sqrt{3}$ Step 3: Combine like terms. $(5 + 4 + 2 - 6)\sqrt{3} = 5\sqrt{3}$ Final answer: $5\sqrt{3}$