[tex]x = 6 - 2 \sqrt{5} [/tex]
[tex]y = 2 \sqrt{5} + 6 = 6 + 2 \sqrt{5} [/tex]
[tex]m_{g} = \sqrt{xy} [/tex]
[tex]m_{g} = \sqrt{(6 - 2 \sqrt{5})(6 + 2 \sqrt{5} )} [/tex]
[tex]m_{g} = \sqrt{ {6}^{2} - {(2 \sqrt{5} )}^{2} } [/tex]
[tex]m_{g} = \sqrt{36 - {2}^{2} \times 5} [/tex]
[tex]m_{g} = \sqrt{36 - 4 \times 5} [/tex]
[tex]m_{g} = \sqrt{36 - 20} [/tex]
[tex]m_{g} = \sqrt{16} [/tex]
[tex]m_{g} = 4[/tex]
