Answer:
15+6+2=23
Step-by-step explanation:
[tex]\sqrt[3]{\frac{9\sqrt{5}}{2\sqrt{3}}\cdot\frac{5\sqrt{2}}{8\sqrt{2}}}\\=\sqrt[3]{\frac{9\sqrt{5}}{2\sqrt{3}}\cdot\frac{5}{8}}\\=\sqrt[3]{\frac{45\sqrt{5}}{16\sqrt{3}}}\\=\sqrt[3]{\frac{45\sqrt{15}}{16}}\\=\sqrt[3]{\frac{3\cdot\sqrt{15^3}}{16}}\\=\frac{\sqrt[3]{3}\cdot\sqrt{15}}{2\cdot\sqrt[3]{2}}\\=\frac{\sqrt[3]{6}\cdot\sqrt{15}}{2}[/tex]
we want it in the form of [tex]\frac{\sqrt{a}\sqrt[3]{b}}{c}[/tex], so a = 15, b=6, c=2
also this is the minimum possible value, as we cannot simplify it further
