\(\left(\sqrt{8+2\sqrt{15}}-\sqrt{7-2\sqrt{10}}\right)\left(\sqrt{3}-\sqrt{2}\right)\\ =\left(\sqrt{\left(\sqrt{5}\right)^2+2\cdot\sqrt{5}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}\right)\left(\sqrt{3}-\sqrt{2}\right)\\ =\left(\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\right)\left(\sqrt{3}-\sqrt{2}\right)\\ =\left(\sqrt{5}+\sqrt{3}-\sqrt{5}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)\\ =\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)\\ =3-2\\ =1\)
\(\left(\sqrt{\left(3-\sqrt{5}\right)^2}+\dfrac{8}{\sqrt{5}-1}\right):\left(\sqrt{5}+1\right)\\ =\left[3-\sqrt{5}+\dfrac{8\left(\sqrt{5}+1\right)}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}\right]:\left(\sqrt{5}+1\right)\\ =\left(3-\sqrt{5}+\dfrac{8\left(\sqrt{5}+1\right)}{4}\right):\left(\sqrt{5}+1\right)\\ =\left(3-\sqrt{5}+2\sqrt{5}+2\right):\left(\sqrt{5}+1\right)\\ =\left(5+\sqrt{5}\right):\left(\sqrt{5}+1\right)\\ =\sqrt{5}\left(\sqrt{5}+1\right):\left(\sqrt{5}+1\right)\\ =\sqrt{5}\)
