[tex]\diaplsyatyle a=3+2 \sqrt{2} \\ \\ b=19(3-2 \sqrt{2} ) \Rightarrow b=57-38 \sqrt{2} \\ \\ m_g= \sqrt{a \cdot b} = \sqrt{\left(3+2 \sqrt{2} \right)\left(57-38 \sqrt{2}\right) } =\\ \\ = \sqrt{171-114 \sqrt{2}+ 114 \sqrt{2}- 152} = \sqrt{171-152} = \sqrt{19} \\ \\ \boxed{m_g= \sqrt{19} }[/tex]
