1. Stating the problem: Simplify the expressions a) $\sqrt{72}$, b) $5\sqrt{8}$, c) $\sqrt{48}$, and d) $2\sqrt{125}$. 2. Important rule: To simplify square roots, factor the number inside the root into perfect squares and other factors, then take the square root of the perfect squares outside the root. 3. Simplify each: - a) $\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$ - b) $5\sqrt{8} = 5 \times \sqrt{4 \times 2} = 5 \times \sqrt{4} \times \sqrt{2} = 5 \times 2 \sqrt{2} = 10\sqrt{2}$ - c) $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$ - d) $2\sqrt{125} = 2 \times \sqrt{25 \times 5} = 2 \times \sqrt{25} \times \sqrt{5} = 2 \times 5 \sqrt{5} = 10\sqrt{5}$ Final answers: - a) $6\sqrt{2}$ - b) $10\sqrt{2}$ - c) $4\sqrt{3}$ - d) $10\sqrt{5}$