Simplify : $$\sqrt {3 + \frac{{33}}{{64}}} \div $$   $$\sqrt {9 + \frac{1}{7}} \times $$   $$2\sqrt {3\frac{1}{9}} $$   = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & \sqrt {3 + \frac{{33}}{{64}}} \div \sqrt {9 + \frac{1}{7}} \times 2\sqrt {3\frac{1}{9}} \cr & = \sqrt {\frac{{225}}{{64}}} \div \sqrt {\frac{{64}}{7}} \times 2\sqrt {\frac{{28}}{9}} \cr & = \sqrt {\frac{{225}}{{64}} \times \frac{7}{{64}} \times \frac{{28}}{9}} \times 2 \cr & = \frac{{5 \times 7}}{{8 \times 4}} \times 2 \cr & = \frac{{35}}{{16}} \cr & = 2\frac{3}{{16}} \cr} $$