Given the fraction;
[tex]\frac{4-\sqrt[]{8}}{10}[/tex]
We shall simplify as follows;
[tex]\begin{gathered} \frac{4-\sqrt[]{8}}{10} \\ \text{Simplify the radical by breaking it down as follows;} \\ \sqrt[]{8}=\sqrt[]{4\times2} \\ \sqrt[]{8}=2\sqrt[]{2} \end{gathered}[/tex]
We can now re-write as;
[tex]\begin{gathered} \frac{4-2\sqrt[]{2}}{10} \\ \text{Factor out the co}mmon\text{ term, which is 2} \\ \frac{2(2-\sqrt[]{2})}{2(5)} \end{gathered}[/tex]
Simplified, this now becomes;
ANSWER:
[tex]\frac{2-\sqrt[]{2}}{5}[/tex]
