Answer
$3.516$
Work Step by Step
Step 1. Let $f(x)=\sqrt x +\sqrt {1+x} -4$, we have $f(0)=0+1-4=-3\lt0$ and $f(4)=2+\sqrt 5-4=\sqrt 5-2\gt0$
Step 2. By using the Intermediate Value Theorem, we know that there is a zero between $x=0$ and $x=4$
Step 3. Graphing the function $f(x)$ as shown, we can find a solution at $x=3.516$
