a) [tex](\sqrt{15}+2\sqrt{3})^2+2\sqrt{5}=15+12\sqrt{5}+12+2\sqrt{5}=27+14\sqrt{5}[/tex]
b)[tex](\sqrt{6}+2)(\sqrt{3}-\sqrt{2})=\sqrt{2}(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})[/tex] [tex]=\sqrt{2}(3-2)=\sqrt{2}[/tex]
c)[tex]\frac{5+7\sqrt{5}}{\sqrt{5}}+\frac{11+\sqrt{11}}{1+\sqrt{11}}[/tex]
[tex]=\frac{\sqrt{5}(\sqrt{5}+7)}{\sqrt{5}}+\frac{\sqrt{11}(\sqrt{11}+1)}{1+\sqrt{11}}[/tex]
[tex]=\sqrt{5}+7+\sqrt{11}[/tex]