The expression shown in the image is:

$\frac{1}{\sqrt{2}} + \sqrt{8}$

To simplify this expression, let's break it down:

1. Simplify the square roots.

   • $\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$
   • So, the expression becomes: $\frac{1}{\sqrt{2}} + 2\sqrt{2}$

2. To simplify the term $\frac{1}{\sqrt{2}}$, multiply both the numerator and denominator by $\sqrt{2}$ to rationalize the denominator: $\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}$

3. Now, the expression is: $\frac{\sqrt{2}}{2} + 2\sqrt{2}$

4. To combine these terms, express $2\sqrt{2}$ with a denominator of 2: $2\sqrt{2} = \frac{4\sqrt{2}}{2}$

5. Now, we can add the fractions: $\frac{\sqrt{2}}{2} + \frac{4\sqrt{2}}{2} = \frac{5\sqrt{2}}{2}$

Thus, the simplified result is:

$\frac{5\sqrt{2}}{2}$

Do you need any further clarification or details? Let me know!

Here are 5 related questions to explore:

1. How to rationalize the denominator in square roots?
2. How to simplify expressions involving square roots?
3. What are common methods to combine fractions with square roots?
4. How to factor numbers inside square roots?
5. What other expressions can be simplified in a similar manner?

Tip: When rationalizing a denominator, multiply by the conjugate if the denominator is a binomial expression.