Rút gọn các biểu thức:
1. \(\sqrt{28}-2\sqrt{252}+3\sqrt{175}+3\sqrt{567}\)
2. \(\sqrt{\left(\sqrt{3}+1\right)^2}+\sqrt{7-4\sqrt{3}}\)
3. \(\sqrt{9-4\sqrt{5}}-\sqrt{\dfrac{8}{7-3\sqrt{5}}}\)
4. \(\dfrac{\sqrt{3}}{2-\sqrt{3}}+\dfrac{2}{2+\sqrt{3}}\)
5. \(\dfrac{2\sqrt{2}+1}{1+\sqrt{2}}+\dfrac{1-2\sqrt{2}}{1-\sqrt{2}}+\left(2-\sqrt{3}\right).\left(2+\sqrt{3}\right)\)
6. \(\sqrt{\dfrac{2}{3-\sqrt{5}}}+\sqrt{\dfrac{2}{7+\sqrt{45}}}\)
7. \(\dfrac{\sqrt{2}}{\sqrt{1+\sqrt{2}}-1}-\dfrac{\sqrt{2}}{\sqrt{1+\sqrt{2}}+1}\)
8. \(\sqrt{6-2\sqrt{5}}+\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}-\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}\)