The value of $$\frac{{\sqrt {72} \times \sqrt {363} \times \sqrt {175} }}{{\sqrt {32} \times \sqrt {147} \times \sqrt {252} }}$$    is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{\sqrt {72} \times \sqrt {363} \times \sqrt {175} }}{{\sqrt {32} \times \sqrt {147} \times \sqrt {252} }} \cr & \Rightarrow \frac{{\sqrt {2 \times 2 \times 2 \times 3 \times 3} \times \sqrt {11 \times 11 \times 3} \times }}{{\sqrt {2 \times 2 \times 2 \times 2 \times 2} \times \sqrt {3 \times 7 \times 7} \times }}\,.\,.\,.\,.\,\frac{{\sqrt {5 \times 5 \times 7} }}{{\sqrt {2 \times 2 \times 3 \times 3 \times 7} }} \cr & \Rightarrow \frac{{6\sqrt 2 \times 11\sqrt 3 \times 5\sqrt 7 }}{{4\sqrt 2 \times 7\sqrt 3 \times 6\sqrt 7 }} \cr & \Rightarrow \frac{{6 \times 11 \times 5}}{{4 \times 7 \times 6}} \cr & \Rightarrow \frac{{55}}{{28}} \cr} $$