$${\text{The value of }}\frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }}{\text{ is?}}$$

A. 5$$\sqrt 3 $$ - 8

B. 5$$\sqrt 5 $$ + 8

C. 8$$\sqrt 3 $$ + 5

D. 8$$\sqrt 3 $$ - 5

Answer: Option A

Solution(By Examveda Team)

$$\frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }}$$
(By rationalization of denominator)
$$\eqalign{ & = \frac{{4 + 3\sqrt 3 }}{{7 + 4\sqrt 3 }} \times \frac{{7 - 4\sqrt 3 }}{{7 - 4\sqrt 3 }} \cr & = \frac{{\left( {4 + 3\sqrt 3 } \right)\left( {7 - 4\sqrt 3 } \right)}}{{49 - 48}} \cr} $$