[tex]\displaystyle\\
a=\frac{4}{ \sqrt{5}-3 } \\\\
b= \frac{2 \sqrt{15} }{ \sqrt{12}} -3=\frac{2 \sqrt{3\times5} }{ \sqrt{4\times3}} -3= \frac{2 \sqrt{3} \times \sqrt{5} }{ 2\sqrt{3}} -3=\sqrt{5}-3\\\\\\
m_g = \sqrt{a\times b} = \sqrt{\frac{4}{ \sqrt{5}-3 } \times (\sqrt{5}-3)} =\sqrt{\frac{4(\sqrt{5}-3)}{ \sqrt{5}-3 } }= \sqrt{4} = \boxed{\bf 2}[/tex]
