\(a,=\dfrac{\sqrt{2}\sqrt{3+\sqrt{5}}}{\sqrt{2}}-\sqrt{3}-\sqrt{5}-\sqrt{2}\\ =\dfrac{\sqrt{6+2\sqrt{5}}}{\sqrt{2}}-\sqrt{3}-\sqrt{5}-\sqrt{2}\\ =\dfrac{\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{6}-\sqrt{10}-2}{\sqrt{2}}\\ =\dfrac{\left|\sqrt{5}+1\right|-\sqrt{6}-\sqrt{10}-2}{\sqrt{2}}\\ =\dfrac{\sqrt{5}+1-\sqrt{6}-\sqrt{10}-2}{\sqrt{2}}=\dfrac{\sqrt{5}-\sqrt{6}-\sqrt{10}-1}{\sqrt{2}}\)
\(b,=\dfrac{\sqrt{2}\sqrt{4-\sqrt{7}}}{\sqrt{2}}-2+2\sqrt{7}\\ =\dfrac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}-2\left(1-\sqrt{7}\right)=\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{2}}-2\left(1-\sqrt{7}\right)\\ =\dfrac{\sqrt{7}-1}{\sqrt{2}}-2\left(1-\sqrt{7}\right)\\ =\dfrac{\sqrt{14}-\sqrt{2}-4\left(1-\sqrt{7}\right)}{2}\\ =\dfrac{\sqrt{14}-\sqrt{2}-4+4\sqrt{7}}{2}\)
