SurdsAQA A-Level Maths: Mind map

Exam questions on Surds

1. Let $p=\sqrt{50}$ and $q=\sqrt{8}$.
   Express $\dfrac{p}{q}$ as a fraction in its simplest form.2 marks
2. A rectangle has length $(3+\sqrt5)$ cm and width $(3-\sqrt5)$ cm.
   Express length divided by width in the form $a+b\sqrt5$, where $a$ and $b$ are rational.2 marks
3. A rectangle has area $(8+2\sqrt7)$ cm$^2$ and length $(\sqrt7-1)$ cm.
   Find the width of the rectangle, giving your answer in the form $\dfrac{a+b\sqrt7}{c}$ where $a$, $b$ and $c$ are integers.3 marks