What is the value of $$\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} = ?$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & \,\,\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} \cr & = \frac{{\sqrt {2 \times 2 \times 6} + \sqrt {6 \times 6 \times 6} }}{{\sqrt {4 \times 4 \times 6} }} \cr & = \frac{{2\sqrt 6 + 6\sqrt 6 }}{{4\sqrt 6 }} \cr & = \frac{8}{4} \cr & = 2 \cr} $$