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.

Another solution
\begin{align*}
\sqrt {49 - x^2} - \sqrt {25 - x^2} &= 3\\
\sqrt {49-x^2} &= 3+ \sqrt {25-x^2}\\
49-x^2 &= 25 -x^2 + 9 + 6\sqrt {25-x^2}\\
15 &= 6 \sqrt {25 - x^2}\\
25 - x^2 &= \frac {25} 4\\
x^2 &= \frac {75}4\\
x &= \pm \frac 5 2 \sqrt 3.
\end{align*}
