[tex]1)m_{a} = \frac{7 - 4 \sqrt{3} + 7 + 4 \sqrt{3} }{2} = \frac{14}{2} = 7[/tex]
[tex]m_{g} = \sqrt{(7 - 4 \sqrt{3})(7 + 4 \sqrt{3} ) } [/tex]
[tex]m_{g} = \sqrt{ {7}^{2} - {(4 \sqrt{3}) }^{2} } [/tex]
[tex]m_{g} = \sqrt{49 - 48} [/tex]
[tex]m_{g} = \sqrt{1} [/tex]
[tex]m_{g} = 1[/tex]
[tex]2)m_{a} = \frac{8 - \sqrt{39} + 8 + \sqrt{39} }{2} = \frac{16}{2} = 8[/tex]
[tex]m_{g} = \sqrt{(8 - \sqrt{39})(8 + \sqrt{39} ) } [/tex]
[tex]m_{g} = \sqrt{ {8}^{2} - {( \sqrt{39}) }^{2} } [/tex]
[tex]m_{g} = \sqrt{64 - 39} [/tex]
[tex]m_{g} = \sqrt{15} [/tex]
[tex]3)m_{a} = \frac{7 - 2 \sqrt{6} + 7 + 2 \sqrt{6} }{2} = \frac{14}{2} = 7[/tex]
[tex]m_{g} = \sqrt{(7 - 2 \sqrt{6})(7 + 2 \sqrt{6} ) } [/tex]
[tex]m_{g} = \sqrt{ {7}^{2} - {(2 \sqrt{6}) }^{2} } [/tex]
[tex]m_{g} = \sqrt{49 - 24} [/tex]
[tex]m_{g} = \sqrt{25} [/tex]
[tex]m_{g} = 5[/tex]
[tex]4)m_{a} = \frac{ 6- 2 \sqrt{5} + 6 + 2 \sqrt{5} }{2} = \frac{12}{2} = 6[/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 - 20} [/tex]
[tex]m_{g} = \sqrt{16} [/tex]
[tex]m_{g} = 4[/tex]
