Solve the given equation. $$\tfrac{3+\sqrt6}{5\sqrt3-2\sqrt{12}-\sqrt{32}+\sqrt{50}}$$​ = ?

Correct option is D

Given:

$$\frac{3+\sqrt6}{5\sqrt3-2\sqrt{12}-\sqrt{32}+\sqrt{50}}$$

Solution:

​​$$\frac{3+\sqrt6}{5\sqrt3-2\sqrt{12}-\sqrt{32}+\sqrt{50}}$$

$$=\frac{3+\sqrt{6}}{5\sqrt{3}-4\sqrt{3}-4\sqrt{2}+5\sqrt{2}}\\=\frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}$$

=$$\frac{\sqrt{3}(\sqrt{3}+\sqrt{2})}{\sqrt{3}+\sqrt{2}}$$

=$$\sqrt{3}$$

Option (D) is right.