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please answer for if x=root5+root3 andy=root6-root2 find value of x^+y^+xy

Dear Student,

Assuming x^+ y^+ 2 xy as x^{2} + y^{2} + 2 xy = {(\sqrt{5} + \sqrt{3})}^{2} + {(\sqrt{6} - \sqrt{2})}^{2} + 2 (\sqrt{5} + \sqrt{3}) (\sqrt{6} - \sqrt{2}) = 5 + 3 + 2 \sqrt{15} + 6 + 2 - 2 \sqrt{12} + 2 (\sqrt{30} - \sqrt{10} + \sqrt{18} - \sqrt{6}) = 16 + 2 \sqrt{15} - 4 \sqrt{3} + 2 (\sqrt{30} - \sqrt{10} + 3 \sqrt{2} - \sqrt{6}) = 16 + 2 \sqrt{15} - 4 \sqrt{3} + 2 \sqrt{30} - 2 \sqrt{10} + 6 \sqrt{2} - 2 \sqrt{6}

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