\documentclass{article} \usepackage{amsmath} \usepackage{multicol} \usepackage{graphicx} \newcommand{\Question}[1]{\item} \newenvironment{solutionordottedlines}[1]{\dotfill}{} \newenvironment{examplebox}{\begin{center}}{\end{center}} \newenvironment{exercisebox}{\begin{center}}{\end{center}} \newcommand{\drawTriangle}[8]{} \begin{document} \begin{solutionordottedlines}[2cm] \end{solutionordottedlines} You must realise that a surd is an \textbf{exact value}, and anything that your calculator spits back at you is only an \emph{approximation In your calculator \(\sqrt{2} = 1.414213562\), but in truth \(\sqrt{2}\) never terminates, it continues forever as it is \emph{irrational}! Let's round some surds to 3 decimal places: \begin{examplebox} \section*{Examples} \begin{multicols}{4} \begin{questions} \Question[1] \(\sqrt{19}=\)\fillin[4.359]{0.7in} \Question[1] \(\sqrt{37}=\)\fillin[6.083]{0.7in} \Question[1] \(\sqrt{161}=\)\fillin[12.688]{0.65in} \Question[1] \(\sqrt{732}=\)\fillin[27.055]{0.65in} \end{questions} \end{multicols} \end{examplebox} Now we shall find the \emph{exact} lengths of the following sides. Realise that unlike before our side lengths are not whole or even \emph{rational} numbers. \end{document}