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1. Evaluate : $\sqrt{20} + \sqrt{12} + \sqrt[3]{729} -$ $\frac{4}{\sqrt{5} - \sqrt{3}} -$ $\sqrt{81} = ?$

A. $\sqrt{2}$

B. $\sqrt{3}$

C. 0

D. $2 \sqrt{2}$

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

\begin{aligned} = 2 \sqrt{5} + 2 \sqrt{3} + 9 - (\frac{4 (\sqrt{5} + \sqrt{3})}{2}) - 9 \\ = 2 \sqrt{5} + 2 \sqrt{3} + 9 - 2 \sqrt{5} - 2 \sqrt{3} - 9 \\ = 0 \end{aligned}

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