[tex]x = (7 + 2 \sqrt{11} )(8 - \sqrt{19} )[/tex]
[tex]y = (8 + \sqrt{19} )(7 - 2 \sqrt{11} )[/tex]
[tex]mg = \sqrt{xy} [/tex]
[tex]mg = \sqrt{(7 + 2 \sqrt{11} )(8 - \sqrt{19} )(8 + \sqrt{19} )(7 - 2 \sqrt{11}) } [/tex]
[tex]mg = \sqrt{( 7+2 \sqrt{11}) ( 7 - 2 \sqrt{11})(8 - \sqrt{19} )(8 + \sqrt{19)} } [/tex]
[tex]mg = \sqrt{[ {7}^{2} - {(2 \sqrt{11} )}^{2}] \times [ {8}^{2} - {( \sqrt{19} )}^{2} ]}[/tex]
[tex]mg = \sqrt{(49 - 44)(64 - 19)} [/tex]
[tex]mg = \sqrt{5 \times 45} [/tex]
[tex]mg = \sqrt{5} \times \sqrt{45} [/tex]
[tex]mg = \sqrt{5} \times 3 \sqrt{5} [/tex]
[tex]mg = 3 \sqrt{25} [/tex]
[tex]mg = 3 \times 5[/tex]
[tex]mg = 15[/tex]
