[tex](2 \sqrt{2} + 3\sqrt{3})^2 = 8 + 12\sqrt{6} + 27 = 35 + 12\sqrt{6} [/tex]
[tex](5\sqrt{3}+4\sqrt{2})(5\sqrt{3}-4\sqrt{2} ) = (5\sqrt{3})^2 - (4\sqrt{2})^2 = 75 -32 = 43 [/tex]
[tex](2 \sqrt{2} - 3\sqrt{3})^2 = 8 - 12\sqrt{6} + 27 = 35 - 12\sqrt{6} [/tex]