[tex] {(4 \sqrt{3} + 5 \sqrt{2} )}^{2} = {(4 \sqrt{3} ) }^{2} + 2 \times 4 \sqrt{3} \times 5 \sqrt{2} + {(5 \sqrt{2} )}^{2} [/tex]
[tex] = {4}^{2} \times 3 + (2 \times 4 \times 5) \sqrt{3 \times 2} + {5}^{2} \times 2[/tex]
[tex] = 16 \times 3 + 40 \sqrt{6} + 25 \times 2[/tex]
[tex] = 48 + 40 \sqrt{6} + 50[/tex]
[tex] = 98 + 40 \sqrt{6} [/tex]
[tex] = 2(49 + 20 \sqrt{6} )[/tex]
