[tex]a) \ (5\frac{2}{3})^{\frac{1}{2}}=(\frac{17}{3})^{\frac{1}{2}}=\sqrt{\frac{17}{3}} = \frac{\sqrt{17}}{\sqrt{3}} \cdot\frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{17\times3}}{3} = \frac{\sqrt{51}}{3}\\\\\\b) \ \sqrt[3]{4}\times\sqrt{8} = (2^{2})^{\frac{1}{3}}\times(2^{3})^{\frac{1}{2}} = 2^{\frac{2}{3}}\times2^{\frac{3}{2}} = 2^{\frac{2}{3}+\frac{3}{2}} = 2^{\frac{13}{6}}[/tex]
[tex]c) \ 3\frac{1}{2}\times2\frac{1}{2} = \frac{7}{2}\times\frac{5}{2} = \frac{35}{4} = 8\frac{3}{4}[/tex]
[tex]d) \ \frac{15\frac{1}{2}}{5\frac{1}{2}} = \frac{\frac{31}{2}}{\frac{11}{2}} = \frac{31}{2}\times\frac{2}{11} = \frac{31}{11} = 2\frac{9}{11}[/tex]
