\(\left(2-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{6}\right)\sqrt{2+\sqrt{3}}\\ =\left(2-\sqrt{3}\right)\left(1+\sqrt{3}\right)\sqrt{4+2\sqrt{3}}\\ =\left(2-\sqrt{3}\right)\left(1+\sqrt{3}\right)\sqrt{3+1+2\sqrt{3}}\\ =\left(2-\sqrt{3}\right)\left(1+\sqrt{3}\right)\sqrt{\left(\sqrt{3}+1\right)^2}\\ =\left(2-\sqrt{3}\right)\left(1+\sqrt{3}\right)\left(\sqrt{3}+1\right)\\ =\left(2-\sqrt{3}\right)\left(1+\sqrt{3}\right)^2\\ =\left(2-\sqrt{3}\right)\left(1+2\sqrt{3}+3\right)\\ =\left(2-\sqrt{3}\right)\left(4+2\sqrt{3}\right)\\ =2\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)\\ =2\left(4-3\right)=2\)
\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\\ =\dfrac{\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}}{\sqrt{2}}\\ =\dfrac{\sqrt{7+1-2\sqrt{7}}-\sqrt{7+1+2\sqrt{7}}}{\sqrt{2}}\\ =\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}\\ =\dfrac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
