Evaluate : $$\sqrt {20} + \sqrt {12} + \root 3 \of {729} \,\, - $$ $$\frac{4}{{\sqrt 5 - \sqrt 3 }} \,- $$ $$\sqrt {81} = ?$$
A. $$\sqrt 2 $$
B. $$\sqrt 3 $$
C. 0
D. $$2\sqrt 2 $$
Answer: Option C
Solution (By Examveda Team)
$$\sqrt {20} + \sqrt {12} + \root 3 \of {729} - \frac{4}{{\sqrt 5 - \sqrt 3 }} - \sqrt {81} $$$$ = 2\sqrt 5 + 2\sqrt 3 + 9\, - $$ $$\left( {\frac{4}{{\sqrt 5 - \sqrt 3 }} \times \frac{{\sqrt 5 + \sqrt 3 }}{{\sqrt 5 + \sqrt 3 }}} \right)$$ $$\, - \,9$$
$$\eqalign{ & = 2\sqrt 5 + 2\sqrt 3 + 9 - \left( {\frac{{4\left( {\sqrt 5 + \sqrt 3 } \right)}}{2}} \right) - 9 \cr & = 2\sqrt 5 + 2\sqrt 3 + 9 - 2\sqrt 5 - 2\sqrt 3 - 9 \cr & = 0 \cr} $$
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