1. The problem is to simplify or understand the expression $\sqrt{2}{x+1}$. 2. The notation $\sqrt{2}{x+1}$ is ambiguous, but it likely means the square root of $x+1$, which is written as $\sqrt{x+1}$. 3. The square root function $\sqrt{y}$ means a number which when squared gives $y$. 4. So, $\sqrt{x+1}$ is the number which when squared equals $x+1$. 5. There is no further simplification unless we know the value of $x$ or additional context. 6. Therefore, the expression $\sqrt{x+1}$ is the simplified form.