1. The problem asks to evaluate the function $g(x) = \sqrt{x} + 2$ for the expression $g(x+h)$ and simplify the answer. 2. The function $g(x)$ is defined as $g(x) = \sqrt{x} + 2$. To find $g(x+h)$, we substitute $x+h$ into the function in place of $x$. 3. Substituting, we get: $$g(x+h) = \sqrt{x+h} + 2$$ 4. This is the simplified form of $g(x+h)$ since the square root cannot be simplified further without specific values for $x$ and $h$. 5. Therefore, the final answer is: $$g(x+h) = \sqrt{x+h} + 2$$