The value of ( 12 - 8 ) ( 3 + 2 )5 + 24 is = ?

Answer: Option C

$$\begin{array}{rl}& \sqrt{\frac{\left(\sqrt{12}-\sqrt{8}\right)\left(\sqrt{3}+\sqrt{2}\right)}{5+\sqrt{24}}}\\ & =\sqrt{\frac{\sqrt{36}+\sqrt{24}-\sqrt{24}-\sqrt{16}}{5+\sqrt{24}}}\\ & =\sqrt{\frac{6-4}{5+\sqrt{24}}}\\ & =\sqrt{\frac{2}{5+\sqrt{24}}\times \frac{5-\sqrt{24}}{5-\sqrt{24}}}\\ & =\sqrt{\frac{2\left(5-\sqrt{24}\right)}{25-24}}\\ & =\sqrt{2\left(5-2\sqrt{6}\right)}\\ & =\sqrt{2\left\{{\left(\sqrt{3}\right)}^2+{\left(\sqrt{2}\right)}^2-2\sqrt{3}\times \sqrt{2}\right\}}\\ & =\sqrt{2{\left(\sqrt{3}-\sqrt{2}\right)}^2}\\ & =\sqrt{2}\left(\sqrt{3}-\sqrt{2}\right)\\ & =\sqrt{6}-2\end{array}$$