The problem asks to rationalize the denominator of the expression:

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

To rationalize the denominator, we need to eliminate the square root from the denominator. We can achieve this by multiplying both the numerator and denominator by $\sqrt{2}$, as follows:

$\frac{5 + \sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{(5 + \sqrt{2}) \times \sqrt{2}}{(\sqrt{2})^2}$

Now, simplify the terms:

1. In the numerator: $(5 + \sqrt{2}) \times \sqrt{2} = 5\sqrt{2} + \sqrt{2} \times \sqrt{2} = 5\sqrt{2} + 2$

2. In the denominator: $(\sqrt{2})^2 = 2$

Thus, the expression becomes:

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

This is the rationalized form of the expression.

Would you like further details or have any questions? Here are some related questions to consider:

1. How can we rationalize more complex denominators?
2. What is the purpose of rationalizing denominators in algebra?
3. How do we handle expressions with multiple radicals?
4. Can we use this technique to rationalize cube roots?
5. What are common mistakes made when rationalizing denominators?

Tip: Always remember to multiply both the numerator and denominator by the same value to keep the expression equivalent.