1. The problem is to simplify the square roots: $\sqrt{128}$, $\sqrt{192}$, $\sqrt{162}$, $\sqrt{243}$, $\sqrt{200}$, $\sqrt{500}$, $\sqrt{12}$, $\sqrt{18}$, $\sqrt{20}$, $\sqrt{45}$, $\sqrt{75}$, and $\sqrt{98}$.\n\n2. The formula to simplify square roots is to factor the number inside the root into its prime factors and extract perfect squares. For example, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, and if $a$ is a perfect square, $\sqrt{a}$ is an integer.\n\n3. Simplify each: \n- $\sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2}$\n- $\sqrt{192} = \sqrt{64 \times 3} = 8\sqrt{3}$\n- $\sqrt{162} = \sqrt{81 \times 2} = 9\sqrt{2}$\n- $\sqrt{243} = \sqrt{81 \times 3} = 9\sqrt{3}$\n- $\sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2}$\n- $\sqrt{500} = \sqrt{100 \times 5} = 10\sqrt{5}$\n- $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$\n- $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$\n- $\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$\n- $\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$\n- $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$\n- $\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}$\n\n4. These simplifications help in easier calculations and understanding of roots.\n\nFinal answers:\n$\sqrt{128} = 8\sqrt{2}$\n$\sqrt{192} = 8\sqrt{3}$\n$\sqrt{162} = 9\sqrt{2}$\n$\sqrt{243} = 9\sqrt{3}$\n$\sqrt{200} = 10\sqrt{2}$\n$\sqrt{500} = 10\sqrt{5}$\n$\sqrt{12} = 2\sqrt{3}$\n$\sqrt{18} = 3\sqrt{2}$\n$\sqrt{20} = 2\sqrt{5}$\n$\sqrt{45} = 3\sqrt{5}$\n$\sqrt{75} = 5\sqrt{3}$\n$\sqrt{98} = 7\sqrt{2}$