Question : Evaluate $\sqrt{20}+\sqrt{12}+\sqrt[3]{729}-\frac{4}{\sqrt{5}-\sqrt{3}}-\sqrt{81}:$
Option 1: $\sqrt{2}$
Option 2: $\sqrt{3}$
Option 3: $0$
Option 4: $2\sqrt{2}$
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Correct Answer: $0$
Solution :
$\sqrt{20}+\sqrt{12}+\sqrt[3]{729}-\frac{4}{\sqrt{5}-\sqrt{3}}-\sqrt{81}$
$=2\sqrt{5}+2\sqrt{3}+9-\frac{4}{\sqrt{5}-\sqrt{3}}\times\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}-9$
$=2(\sqrt{5}+\sqrt{3})-\frac{4\times(\sqrt{5}+\sqrt{3})}{5-3}$
$=(\sqrt{5}+\sqrt{3})(2-2)$
$=0$
Hence, the correct answer is $0$.
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