To simplify the expression $\frac{7}{\sqrt{2}}$ with a rational denominator, we need to "rationalize" the denominator. This is done by multiplying both the numerator and the denominator by $\sqrt{2}$, the square root in the denominator. Here are the steps:

$\frac{7}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7\sqrt{2}}{2}$

So, the expression simplifies to:

$\frac{7\sqrt{2}}{2}$

This is the simplest form with a rational denominator.

Would you like further clarification, or have any questions? Here are some related questions:

1. What is the process of rationalizing a denominator?
2. Why can't we leave a square root in the denominator?
3. How would this process change for higher-order roots, like cube roots?
4. What is an example of rationalizing a binomial denominator (e.g., $\frac{1}{\sqrt{3} + 2}$)?
5. How can this concept be applied in complex fractions?

Tip: Rationalizing the denominator helps in standardizing the form of an expression, making it easier for further operations.