[tex]a=\frac{\sqrt{28}-\sqrt{20}}{\sqrt3+1}\\
a=\frac{2\sqrt7-2\sqrt5}{\sqrt3+1}\\
a=\frac{2(\sqrt7-\sqrt5)(\sqrt3-1)}{(\sqrt3+1)(\sqrt3-1)}\\
a=\frac{2(\sqrt7-\sqrt5)(\sqrt3-1)}{3-1}\\
a=\frac{2(\sqrt7-\sqrt5)(\sqrt3-1)}{2}\\
a=(\sqrt7-\sqrt5)(\sqrt3-1)[/tex]
[tex]b=\frac{\sqrt{12}+2}{\sqrt7-\sqrt5}\\
b=\frac{2\sqrt3+2}{\sqrt7-\sqrt5}\\
b=\frac{2(\sqrt3+1)(\sqrt7+\sqrt5)}{(\sqrt7-\sqrt5)(\sqrt7+\sqrt5)}\\
b=\frac{2(\sqrt3+1)(\sqrt7+\sqrt5)}{7-5}\\
b=\frac{2(\sqrt3+1)(\sqrt7+\sqrt5)}{2}\\
b=(\sqrt3+1)(\sqrt7+\sqrt5)\\
m_g=\sqrt{ab}\\
m_g=\sqrt{(\sqrt3-1)(\sqrt3+1)(\sqrt7-\sqrt5)(\sqrt7+\sqrt5)}\\
m_g=\sqrt{(3-1)(7-5)}\\
m_g=\sqrt{2^2}\Rightarrow \boxed{\boxed{m_g=2}}[/tex]