[tex]\displaystyle\it\\\sqrt{(a-\sqrt{20})^2}+\sqrt{(b+\sqrt{80})^2}+\sqrt{(c-\sqrt{180})^2}} \leq 0.\\dar,~\begin{cases} \sqrt{(a-\sqrt{20})^2} \geq 0 \\ \sqrt{(b+\sqrt{80})^2} \geq 0\\\sqrt{(c-\sqrt{180})^2}}\geq 0\end{cases} \implies \begin{cases} \sqrt{(a-\sqrt{20})^2}=0\\ \sqrt{(b+\sqrt{80})^2}=0\\ \sqrt{(c-\sqrt{180})^2}=0 \end{cases} \implies\\\begin{cases} a-\sqrt{20}=0 \\b+\sqrt{80}=0\\c-\sqrt{180}=0\end{cases} \implies \begin{cases} a=\sqrt{20}\\b=-\sqrt{80}\\c=\sqrt{180} \end{cases}\implies[/tex]
[tex]\displaystyle\it\\\begin{cases}a=2\sqrt{5}\\b=-4\sqrt{5}\\c=6\sqrt{5} \end{cases}\implies asadar,~a+b+c=2\sqrt{5}-4\sqrt{5}+6\sqrt{5}=\boxed{\it4\sqrt{5}}.[/tex]
