Question

Rewrite the fraction as a single simplified fraction with at most one radical term containing no perfect square factors.

Answer 1

Given the fraction;

`\frac{4-\sqrt[]{8}}{10}`

We shall simplify as follows;

`\begin{gathered} \frac{4-\sqrt[]{8}}{10} \\ \text{Simplify the radical by breaking it down as follows;} \\ \sqrt[]{8}=\sqrt[]{4*2} \\ \sqrt[]{8}=2\sqrt[]{2} \end{gathered}`

We can now re-write as;

`\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}`

Simplified, this now becomes;

ANSWER:

`\frac{2-\sqrt[]{2}}{5}`