Answer
$\{0,9\}$
Work Step by Step
Step 1. Given the equation $\sqrt {x}+2=\sqrt {4+7\sqrt x}$
Step 2. Take square on both sides to get: $x+4\sqrt {x}+4=4+7\sqrt x$ or $x=3\sqrt x$
Step 3. Take square on both sides again to get: $x^2=9x$ or $x^2-9x=0$ which gives $x=0,9$
Step 4. Check answers in the original equation: both $\{0,9\}$ fit.
