In today's lesson we are going to begin by reviewing \textbf{Pythagoras' Theorem} which you should have been introduced to in Year 8, and then delve deeper. We will examine how ``\emph{irrational}" numbers pop out, what the significance of such numbers are, and what the converse of this theorem states. 
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We will also learn the arithmetic of surds: i.e. what can be done with $ \sqrt{8} + 2\sqrt{2} $ and $ \sqrt{3} \div \sqrt{6} $.
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Next week, we shall tackle more complex and less trivial problems of \emph{rationalising the denominator} and \emph{3D trigonometry}!