Given that 3 = 1.732 , the value of 3 + 6 5 3 - 2 12 - 32 + 50 is ?

Answer: Option B

$$\begin{array}{rl}& \text{Given expression,}\\ & =\frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{12}-\sqrt{32}+\sqrt{50}}\\ & =\frac{3+\sqrt{6}}{5\sqrt{3}-4\sqrt{3}-4\sqrt{2}+5\sqrt{2}}\\ & =\frac{\left(3+\sqrt{6}\right)}{\left(\sqrt{3}+\sqrt{2}\right)}\\ & =\frac{\left(3+\sqrt{6}\right)}{\left(\sqrt{3}+\sqrt{2}\right)}\times \frac{\left(\sqrt{3}-\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)}\\ & =\frac{3\sqrt{3}-3\sqrt{2}+3\sqrt{2}-2\sqrt{3}}{\left(3-2\right)}\\ & =\sqrt{3}\\ & =1.732\end{array}$$