Make me SIMPLE DIRECTION: Write each radical in simplest form. \( \begin{array}{lll}\text { 1. } \sqrt{\frac{9}{16}} & \text { 4. } \frac{2}{\sqrt{2}} \\ \text { 2. } \frac{\sqrt{25}}{\sqrt{100}} & \text { 5. } & -\frac{1}{3 \sqrt{2}} \\ \text { 3. } & -\sqrt{\frac{4}{5}}\end{array} \)

Sure! Let's simplify each radical step by step. ### 1. \( \sqrt{\frac{9}{16}} \) \[ \sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4} \] **Simplified Form:** \( \frac{3}{4} \) --- ### 2. \( \frac{\sqrt{25}}{\sqrt{100}} \) \[ \frac{\sqrt{25}}{\sqrt{100}} = \frac{5}{10} = \frac{1}{2} \] **Simplified Form:** \( \frac{1}{2} \) --- ### 3. \( -\sqrt{\frac{4}{5}} \) First, simplify the square root: \[ -\sqrt{\frac{4}{5}} = -\frac{\sqrt{4}}{\sqrt{5}} = -\frac{2}{\sqrt{5}} \] To rationalize the denominator: \[ -\frac{2}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = -\frac{2\sqrt{5}}{5} \] **Simplified Form:** \( -\frac{2\sqrt{5}}{5} \) --- ### 4. \( \frac{2}{\sqrt{2}} \) Rationalize the denominator: \[ \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2} \] **Simplified Form:** \( \sqrt{2} \) --- ### 5. \( -\frac{1}{3\sqrt{2}} \) Rationalize the denominator: \[ -\frac{1}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{3 \times 2} = -\frac{\sqrt{2}}{6} \] **Simplified Form:** \( -\frac{\sqrt{2}}{6} \) --- ### Summary of Simplified Radicals 1. \( \frac{3}{4} \) 2. \( \frac{1}{2} \) 3. \( -\frac{2\sqrt{5}}{5} \) 4. \( \sqrt{2} \) 5. \( -\frac{\sqrt{2}}{6} \)