[tex]a) \ 3\sqrt{5}+4\sqrt{5} = 7\sqrt{5}[/tex]
[tex]b) \ \sqrt{44}\cdot\sqrt{3\frac{2}{3}} =\sqrt{44\cdot\frac{11}{3}} = \sqrt{\frac{484}{3}}=\frac{\sqrt{484}}{\sqrt{3}} = \frac{22}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = \frac{22\sqrt{3}}{3}[/tex]
[tex]c) \ \sqrt{300}-7\sqrt{3} = \sqrt{100\cdot3}-7\sqrt{3} = 10\sqrt{3}-7\sqrt{3} = 3\sqrt{3}[/tex]
[tex]d) \ 3\sqrt{6}\cdot\frac{1}{2}\sqrt{2} =3\cdot\frac{1}{2}\sqrt{6\cdot2} = \frac{3}{2}\sqrt{12} = \frac{3}{2}\sqrt{4\cdot3} = \frac{3}{2}\cdot2\sqrt{3} = 3\sqrt{3}[/tex]
[tex]e) \ (\frac{4\sqrt{6}}{3})^{2} = \frac{4^{2}\cdot\sqrt{6}^{2}}{3^{2}} = \frac{16\cdot6}{9} = \frac{16\cdot2}{3} =\frac{32}{3} = 10\frac{2}{3}[/tex]
