The simplified value of $$\frac{{\sqrt {32} + \sqrt {48} }}{{\sqrt 8 + \sqrt {12} }}{\text{ is = ?}}$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & \frac{{\sqrt {32} + \sqrt {48} }}{{\sqrt 8 + \sqrt {12} }} \cr & = \frac{{\sqrt {4 \times 4 \times 2} + \sqrt {4 \times 4 \times 3} }}{{\sqrt {2 \times 2 \times 2} + \sqrt {2 \times 2 \times 3} }} \cr & = \frac{{4\sqrt 2 + 4\sqrt 3 }}{{2\sqrt 2 + 2\sqrt 3 }} \cr & = \frac{{4\left( {\sqrt 2 + \sqrt 3 } \right)}}{{2\left( {\sqrt 2 + \sqrt 3 } \right)}} \cr & = \frac{4}{2} \cr & = 2 \cr} $$