Question 1: \((i)\) \(\quad\) \(\large{\frac{13}{4+\sqrt{3}}} \)
Solution:
\[\begin{align*}
\frac{13}{4+\sqrt{3}}&=\frac{13}{4+\sqrt{3}} \times \frac{4-\sqrt{3}}{4-\sqrt{3}}\\
&=\frac{13\left( 4-\sqrt{3}\right)}{4^{2} -\left(\sqrt{3}\right)^{2}}\\
&=\frac{13\left( 4-\sqrt{3}\right)}{16-3}\\
&=\frac{13\left( 4-\sqrt{3}\right)}{13}\\
&=4-\sqrt{3}\\
\end{align*}\]