2025 NASS P2 Q1

Without using a calculator, express \(5\sqrt{108}-\sqrt{243}+\dfrac{\sqrt{192}}2\) in the form \(a\sqrt3\), where \(a\) is an integer.[2]

Given that \(p=\sqrt5+2\), express \(\dfrac{p+2}{p-1}\) in the form of \(a\sqrt5+b\), where \(a\) and \(b\) are rational numbers.[3]