Moderate -0.8 This is a standard surds rationalisation question requiring multiplication by the conjugate and simplification. While it involves multiple algebraic steps and careful arithmetic, it's a routine technique taught early in AS-level with no problem-solving insight required—just methodical application of (a+b)(a-b)=a²-b² and collecting like terms. The 4 marks reflect working rather than conceptual difficulty.
Express \(\frac{\sqrt{3} + 3\sqrt{5}}{\sqrt{5} - \sqrt{3}}\) in the form \(a + b\sqrt{c}\), where \(a\) and \(b\) are integers.
Fully justify your answer.
[4 marks]
Express $\frac{\sqrt{3} + 3\sqrt{5}}{\sqrt{5} - \sqrt{3}}$ in the form $a + b\sqrt{c}$, where $a$ and $b$ are integers.
Fully justify your answer.
[4 marks]
\hfill \mbox{\textit{AQA AS Paper 1 2024 Q3 [4]}}