1. The problem is to understand the expression $x = 3 + \sqrt{8}$ and simplify it if possible. 2. Recall that $\sqrt{8}$ means the square root of 8, which can be simplified by factoring 8 into $4 \times 2$. 3. Using the property of square roots, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we get: $$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$$ 4. Substitute back into the expression for $x$: $$x = 3 + 2\sqrt{2}$$ 5. This is the simplified form of $x$. It cannot be simplified further because $\sqrt{2}$ is irrational. Final answer: $$x = 3 + 2\sqrt{2}$$