The value of $x$ satisfying √$(x+5)$ + √$x=5$ is:

Isolate one radical: √$(x+5)=5$ − √$x$. Squaring gives $x+5=25-10$√$x+x$, so 10√$x=20$, √$x=2$ and $x=4$. (16 comes from matching the 5 to the wrong radical and taking √$x=4$; 9 comes from stopping at $x+5=9$.) Check: √9 + √4 = 3 + 2 = 5.