Answer
$\{4\}$
Work Step by Step
Step 1. Given the equation $3-\sqrt {x}=\sqrt {2\sqrt x-3}$
Step 2. Take square on both sides to get: $9-6\sqrt {x}+x=2\sqrt x-3$ or $x+12=8\sqrt x$
Step 3. Take square on both sides again to get: $x^2+24x+144=64x$ or $x^2-40x+144=0$ which gives $x=4,36$
Step 4. Check answers in the original equation: only $\{4\}$ fits.
