Surds and exact calculation

By the end you’ll be able to

• Simplify surds using $\sqrt{ab} = \sqrt{a}\sqrt{b}$, e.g. $\sqrt{72} = 6\sqrt{2}$, and collect like surds
• Expand and simplify brackets containing surds, including $(a + \sqrt{b})(a - \sqrt{b})$
• Rationalise denominators of the form $\frac{1}{\sqrt{a}}$ and $\frac{1}{a + \sqrt{b}}$ (Higher)
• Give exact answers in surd form or in terms of $\pi$ in mensuration, Pythagoras and trigonometry problems