[tex]a=( \sqrt{5}-1 )(1+ \sqrt{10})=( \sqrt{5}-1 )(\sqrt{10}+1) \\ b = (\sqrt{10}-1)(1+ \sqrt{5})=(\sqrt{10}-1)( \sqrt{5}+1) \\ \\ m_g= \sqrt{ab}=\sqrt{( \sqrt{5}-1 )(\sqrt{10}+1)*(\sqrt{10}-1)( \sqrt{5}+1)}= \\ \\ = \sqrt{( \sqrt{5}-1 )( \sqrt{5}+1)*(\sqrt{10}+1)(\sqrt{10}-1)}= \\ \\ = \sqrt{( 5-1 )*(10-1)}=\sqrt{4*9}=\sqrt{36}=\boxed{6}[/tex]
