\(f\left(a\right)=\dfrac{a^2+8}{\sqrt{a^2+4}}=\dfrac{a^2+4}{\sqrt{a^2+4}}+\dfrac{4}{\sqrt{a^2+4}}=\sqrt{a^2+4}+\dfrac{4}{\sqrt{a^2+4}}\)
Áp dụng BĐT Cô-si:
\(f\left(a\right)=\sqrt{a^2+4}+\dfrac{4}{\sqrt{a^2+4}}\ge4\)
\(minf\left(a\right)=4\Leftrightarrow a=0\)