Let us now try to solve the problem from the start of the lesson: $\sqrt{8} + 2\sqrt{2}$. We know from the previous section we can simplify $\sqrt{8}$ into \fillin[$2\sqrt{2}$] and so our expression becomes \fillin[$2\sqrt{2} + 2\sqrt{2}$]. Now recall from last week that we can add \textbf{like terms} together such that our final answer becomes \fillin[$4\sqrt{2}$].

The process for subtraction is exactly the same, and the way to get better at this arithmetic is by doing lots of exercises!

 \begin{exercisebox}                                                                                                                         
     \section{Exercises}                                                                                                                    
         \begin{questions}                                                                                                                   
             \Question[12]                                                                                                                   
             \begin{parts}\begin{multicols}{2}                                                                                               
             \part \[4\sqrt{7} + 5\sqrt{7}=\]                                                                                                
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $9\sqrt{7}$                                                                                                                 
                 \end{solutionordottedlines}                                                                                                 
             \part \[6\sqrt{7}-2\sqrt{7}=\]                                                                                                  
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $4\sqrt{7}$                                                                                                                 
                 \end{solutionordottedlines}                                                                                                 
             \part \[2\sqrt{2}+5\sqrt{2}-3\sqrt{2}=\]                                                                                        
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $4\sqrt{2}$                                                                                                                 
                 \end{solutionordottedlines}                                                                                                 
             \part \[3\sqrt{5}+2\sqrt{7}-\sqrt{5}+4\sqrt{7}=\]                                                                               
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $2\sqrt{5}+6\sqrt{7}$                                                                                                       
                 \end{solutionordottedlines}                                                                                                 
             \part \[\sqrt{27}+2\sqrt{5}+\sqrt{20}-2\sqrt{3}=\]                                                                              
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $3\sqrt{3}+2\sqrt{5}+2\sqrt{5}-2\sqrt{3} = \sqrt{3}+4\sqrt{5}$                                                              
                 \end{solutionordottedlines}                                                                                                 
             \part \[\frac{\sqrt{3}}{2}+3\sqrt{3}=\]                                                                                         
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $\frac{1}{2}\sqrt{3}+\frac{6}{2}\sqrt{3} = \frac{7}{2}\sqrt{3}$                                                             
                 \end{solutionordottedlines}                                                                                                 
             \part \[6\sqrt{2} + 4\sqrt{2}=\]                                                                                                
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $10\sqrt{2}$                                                                                                                
                 \end{solutionordottedlines}                                                                                                 
             \part \[10\sqrt{7}-5\sqrt{7}=\]                                                                                                 
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $5\sqrt{7}$                                                                                                                 
                 \end{solutionordottedlines}                                                                                                 
             \part \[3\sqrt{11}-5\sqrt{11}=\]                                                                                                
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $-2\sqrt{11}$                                                                                                               
                 \end{solutionordottedlines}                                                                                                 
             \part \[2\sqrt{2}+3\sqrt{2}+\sqrt{2}=\]                                                                                         
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $6\sqrt{2}$                                                                                                                 
                 \end{solutionordottedlines}                                                                                                 
             \part \[10\sqrt{5}-\sqrt{5}-6\sqrt{5}=\]                                                                                        
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $3\sqrt{5}$                                                                                                                 
                 \end{solutionordottedlines}                                                                                                 
             \part \[\sqrt{7}-8\sqrt{7}+5\sqrt{7}=\]                                                                                         
                 \begin{solutionordottedlines}[2cm]                                                                                          
                 $-2\sqrt{7}$                                                                                                                
                 \end{solutionordottedlines}                                                                                                 
         \end{multicols}\end{parts}                                                                                                          
         \end{questions}                                                                                                                     
 \end{exercisebox}                                                                                                                           
