$\sqrt[]{x^2-4}+ \sqrt[]{x^2+4x+4}=0 $
$⇒\sqrt[]{(x-2)(x+2)} +\sqrt[]{(x+2)^2}=0 $
$⇒\sqrt[]{x+2} (x-2+x+2)=0$
$⇒2x.\sqrt[]{x+2}=0 $
$⇒\left[ \begin{array}{l}2x=0\\\sqrt[]{x+2} =0\end{array} \right.$
$⇒\left[ \begin{array}{l}x=0\\x+2=0\end{array} \right.$
$⇒\left[ \begin{array}{l}x=0\\x=-2\end{array} \right.$
Vậy $x=0; -2$