a)$\sqrt{\frac{2-\sqrt{3}}{2}}=\sqrt{\frac{4-2\sqrt{3}}{4}}=\sqrt{\frac{(\sqrt{3}-1)^{2}}{4}}=\frac{\sqrt{3}-1}{2}$
b)$\sqrt{\frac{4-\sqrt{7}}{2}}=\sqrt{\frac{8-2\sqrt{7}}{4}}=\sqrt{\frac{(\sqrt{7}-1)^{2}}{4}}=\frac{\sqrt{7}-1}{2}$
c)$\sqrt{\frac{2}{3-\sqrt{5}}}=\sqrt{\frac{4}{6-2\sqrt{5}}}=\sqrt{\frac{4}{(\sqrt{5}-1)^{2}}}=\frac{2}{\sqrt{5}-1}=\frac{\sqrt{5}+1}{2}$
d)$\sqrt{\frac{2}{6+\sqrt{11}}}=\sqrt{\frac{4}{12+2\sqrt{11}}}=\sqrt{\frac{4}{(\sqrt{11}+1)^{2}}}=\frac{2}{\sqrt{11}+1}=\frac{\sqrt{11}-1}{5}$
