[tex]m_g=\sqrt{ x\cdot y}=\\
\sqrt{(\sqrt2-1)\sqrt2+1)(\sqrt7-\sqrt6)(\sqrt7+\sqrt6)(\sqrt9-\sqrt5)(\sqrt9+\sqrt5)}\\\cdot\sqrt{(4-\sqrt7)(4+\sqrt7)}=\sqrt{(2-1)(7-6)(9-5)(16-7)}=\sqrt{4\cdot9}=6\\
m_g=\sqrt{ x\cdot y}=\sqrt{\sqrt{7-4\sqrt3}\sqrt{7-4\sqrt3}}=\sqrt{\sqrt{7^2-(4\sqrt3)^2}}=\\
\sqrt{\sqrt{49-48}}=\sqrt{\sqrt1}=1\\
c)x=\sqrt{(3+2\sqrt3)^2}=|3+2\sqrt3|=3+2\sqrt3\\
\ \ \ y=\sqrt{21-12\sqrt3}=\sqrt{12-2\cdot3\cdot2\sqrt3+9}=\sqrt{(2\sqrt3)^2-2\cdot3\cdot2\sqrt3+3^2}\\
[/tex]
[tex]=\sqrt{(2\sqrt3-3)^2}=2\sqrt3-3\\
m_g=\sqrt{xy}=\sqrt{(2\sqrt3+3)}{(2\sqrt3-3)}=\sqrt{12-9}=\sqrt3[/tex]
