Create and solve two problems involving addition, subtraction, multiplication, and division of radicals. The two problems combined should contain all four operations. For example, one problem could combine addition and multiplication and the second problem could contain subtraction and division. Check out the following sample problem to help you get started.

Sure! Let's create two problems involving all four operations (addition, subtraction, multiplication, and division) of radicals.

### Problem 1: Addition and Multiplication
Let's solve the following problem:

\[
\sqrt{8} + 3 \cdot \sqrt{2} + \sqrt{18}
\]

We can simplify the radicals first:

- \(\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}\)
- \(\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}\)

Substituting back into the equation:

\[
2\sqrt{2} + 3\sqrt{2} + 3\sqrt{2}
\]

Now, combine the like terms:

\[
(2 + 3 + 3)\sqrt{2} = 8\sqrt{2}
\]

So, the solution to Problem 1 is:

\[
\sqrt{8} + 3 \cdot \sqrt{2} + \sqrt{18} = 8\sqrt{2}
\]

### Problem 2: Subtraction and Division
Now let's tackle the following problem:

\[
\sqrt{50} - \frac{\sqrt{18}}{\sqrt{2}}
\]

We will simplify each term.

1. Simplifying \(\sqrt{50}\):
\[
\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}
\]

2. Simplifying \(\frac{\sqrt{18}}{\sqrt{2}}\):
\[
\frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9} = 3
\]

Now substituting these back into the expression:

\[
5\sqrt{2} - 3
\]

This is as simplified as it gets. Therefore, the solution to Problem 2 is:

\[
\sqrt{50} - \frac{\sqrt{18}}{\sqrt{2}} = 5\sqrt{2} - 3
\]

### Summary of Solutions:
- **Problem 1**: \(\sqrt{8} + 3 \cdot \sqrt{2} + \sqrt{18} = 8\sqrt{2}\)
- **Problem 2**: \(\sqrt{50} - \frac{\sqrt{18}}{\sqrt{2}} = 5\sqrt{2} - 3\)

These problems demonstrate the addition, multiplication, subtraction, and division of radicals while simplifying correctly.