a)$ (\sqrt{\dfrac{3}{8}} - \sqrt{24} + \sqrt{\dfrac{50}{3}})\sqrt{6}$
$= (\dfrac{\sqrt{3}}{2\sqrt{2}} - 2 \sqrt{6} + \dfrac{5 \sqrt{2}}{\sqrt{3}}) \sqrt{6}$
$= \dfrac{3}{2} - 12 + 10 = -\dfrac{1}{2}$
b)$(\dfrac{1}{5 - 2 \sqrt{6}} + \dfrac{2}{5 + 2 \sqrt{6}}) (15 + 2 \sqrt{6})$
$= \dfrac{5 + 2 \sqrt{6} + 5 - 2 \sqrt{6}}{(5 - 2 \sqrt{6})(5 + 2 \sqrt{6})}) (15 + 2\sqrt{6})$
$= \dfrac{10}{25-24} (15 + 2 \sqrt{6}) $
$ = 150 + 20 \sqrt{6}$.
c) $\sqrt{13 + 30\sqrt{9 + 4 \sqrt{2}}}$
$= \sqrt{13 + 30 \sqrt{8 + 2 . (2 \sqrt{2}) .1 + 1}}$
$ = \sqrt{13 + 30 \sqrt{(2\sqrt{2} + 1)^2}}$
$ = \sqrt{13 + 30 (2\sqrt{2} + 1)}$
$= \sqrt{43 + 60 \sqrt{2}}$
