Question 1: \((v)\) \(\quad\) \(\large{\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}}\)
Solution:
\[\begin{align*}
\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}} &=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}} \times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}} \\
& =\frac{\left (\sqrt{3}-\sqrt{2}\right)^2}{\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2}\\
&=\small{\frac{\left(\sqrt{3}\right)^2+\left(\sqrt{2}\right)^2-2\sqrt{2}\sqrt{3}}{3-2}}\\
&=\frac{3+2-2\sqrt{2\times3}}{1}\\
&=5-2\sqrt{6}\\
\end{align*}\]