\( \frac{\text { Division }}{\text { 1) } \frac{\sqrt{32}}{\sqrt{2}}} \) 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 break these calculations down and simplify them for a clearer understanding. 1) \( \frac{\sqrt{32}}{\sqrt{2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 \). 2) For \( \frac{\sqrt[3]{51}}{\sqrt[3]{3}} \), this simplifies to \( \sqrt[3]{\frac{51}{3}} = \sqrt[3]{17} \) since \( 51 \div 3 = 17 \). 3) \( \frac{\sqrt{6}}{\sqrt{3}} = \sqrt{\frac{6}{3}} = \sqrt{2} \). 4) Here, \( \frac{\sqrt{39}}{\sqrt{3}} = \sqrt{\frac{39}{3}} = \sqrt{13} \). 5) For \( \frac{3 \sqrt{21}}{\sqrt{7}} \), we can simplify it to \( 3 \sqrt{\frac{21}{7}} = 3 \sqrt{3} \) since \( 21 \div 7 = 3 \). 6) Finally, \( \frac{4 \sqrt{72}}{2 \sqrt{8}} = \frac{4}{2} \cdot \frac{\sqrt{72}}{\sqrt{8}} = 2 \cdot \sqrt{\frac{72}{8}} = 2 \cdot \sqrt{9} = 2 \cdot 3 = 6 \). With a hint of math magic, all these expressions not only simplify beautifully but reveal the elegant relationships behind square and cube roots! Math isn’t just about numbers; it’s like a puzzle where every piece clicks into place! Ready to dive deeper? Try experimenting with combining these roots in different operations, and you might discover even more dazzling simplifications!