\( \frac{\text { Division }}{\text { 1) } \frac{\sqrt{32}}{\sqrt{2}}} \) 2) \( \frac{\sqrt[3]{51}}{\sqrt[3]{3}} \) 3) \( \frac{\sqrt{6}}{\sqrt{3}} \) 4) \( \frac{\sqrt{39}}{\sqrt{3}} \) \( \begin{array}{ll}\text { 5) } \frac{3 \sqrt{21}}{\sqrt{7}} & \text { 6) } \frac{4 \sqrt{72}}{2 \sqrt{8}}\end{array} \)

Let's simplify each of the given division expressions involving square roots and cube roots. ### 1) \( \frac{\sqrt{32}}{\sqrt{2}} \) **Simplification:** \[ \frac{\sqrt{32}}{\sqrt{2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 \] **Answer:** \(4\) --- ### 2) \( \frac{\sqrt[3]{51}}{\sqrt[3]{3}} \) **Simplification:** \[ \frac{\sqrt[3]{51}}{\sqrt[3]{3}} = \sqrt[3]{\frac{51}{3}} = \sqrt[3]{17} \] **Answer:** \( \sqrt[3]{17} \) --- ### 3) \( \frac{\sqrt{6}}{\sqrt{3}} \) **Simplification:** \[ \frac{\sqrt{6}}{\sqrt{3}} = \sqrt{\frac{6}{3}} = \sqrt{2} \] **Answer:** \( \sqrt{2} \) --- ### 4) \( \frac{\sqrt{39}}{\sqrt{3}} \) **Simplification:** \[ \frac{\sqrt{39}}{\sqrt{3}} = \sqrt{\frac{39}{3}} = \sqrt{13} \] **Answer:** \( \sqrt{13} \) --- ### 5) \( \frac{3 \sqrt{21}}{\sqrt{7}} \) **Simplification:** \[ \frac{3 \sqrt{21}}{\sqrt{7}} = 3 \times \frac{\sqrt{21}}{\sqrt{7}} = 3 \times \sqrt{\frac{21}{7}} = 3 \times \sqrt{3} = 3\sqrt{3} \] **Answer:** \( 3\sqrt{3} \) --- ### 6) \( \frac{4 \sqrt{72}}{2 \sqrt{8}} \) **Simplification:** \[ \frac{4 \sqrt{72}}{2 \sqrt{8}} = \frac{4}{2} \times \frac{\sqrt{72}}{\sqrt{8}} = 2 \times \sqrt{\frac{72}{8}} = 2 \times \sqrt{9} = 2 \times 3 = 6 \] **Answer:** \(6\) --- **Summary of Simplified Expressions:** 1. \(4\) 2. \( \sqrt[3]{17} \) 3. \( \sqrt{2} \) 4. \( \sqrt{13} \) 5. \( 3\sqrt{3} \) 6. \(6\)