How to solve $\sqrt{49-x^2}-\sqrt{25-x^2}=3$? I recognize the two difference of squares: $49-x^2$ and $25-x^2$.
I squared the equation to get:
${49-x^2}-2(\sqrt{(49-x^2)(25-x^2)})+{25-x^2}=9$
However, I can't quite figure out how to remove the root in the middle. Any help is appreciated.

First express one root: $$\sqrt{49-x^2}=3+\sqrt{25-x^2}$$
Now square:
$$ 49-x^2=9+6\sqrt{25-x^2}+ 25-x^2\implies \boxed{5=2\sqrt{25-x^2}}$$
and square again...
