The approximate value of $$\frac{{3\sqrt {12} }}{{2\sqrt {28} }}$$  $$ \div $$ $$\frac{{2\sqrt {21} }}{{\sqrt {98} }}$$   is ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Given expression,}} \cr & = \frac{{3\sqrt {12} }}{{2\sqrt {28} }} \times \frac{{\sqrt {98} }}{{2\sqrt {21} }} \cr & = \frac{{3\sqrt {4 \times 3} }}{{2\sqrt {4 \times 7} }} \times \frac{{\sqrt {49 \times 2} }}{{2\sqrt {21} }} \cr & = \frac{{6\sqrt 3 }}{{4\sqrt 7 }} \times \frac{{7\sqrt 2 }}{{2\sqrt {21} }} \cr & = \frac{{21\sqrt 6 }}{{4\sqrt {7 \times 21} }} \cr & = \frac{{21\sqrt 6 }}{{28\sqrt 3 }} \cr & = \frac{3}{4}\sqrt 2 \cr & = \frac{3}{4} \times 1.414 \cr & = 3 \times 0.3535 \cr & = 1.0605 \cr} $$