\(\dfrac{1}{2-\sqrt{3}}+\dfrac{1}{2+\sqrt{3}}-\sqrt{37-20\sqrt{3}}\)
\(=\dfrac{2+\sqrt{3}+2-\sqrt{3}}{4-3}-\sqrt{25-2\cdot5\cdot2\sqrt{3}+12}\)
\(=4-\sqrt{\left(5-2\sqrt{3}\right)^2}=4-\left(5-2\sqrt{3}\right)=2\sqrt{3}-1\)
\(\sqrt{9-4\sqrt{5}}-\dfrac{2}{\sqrt{5}-2}+\dfrac{8}{\sqrt{14-6\sqrt{5}}}\)
\(=\sqrt{\left(\sqrt{5}-2\right)^2}-\dfrac{2\left(\sqrt{5}+2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}+\dfrac{8}{\sqrt{\left(3-\sqrt{5}\right)^2}}\)
\(=\sqrt{5}-2-2\left(\sqrt{5}+2\right)+\dfrac{8}{3-\sqrt{5}}\)
\(=\sqrt{5}-2-2\sqrt{5}-4+\dfrac{8\left(3+\sqrt{5}\right)}{4}\)
\(=-\sqrt{5}-6+2\left(3+\sqrt{5}\right)=-\sqrt{5}-6+6+2\sqrt{5}=\sqrt{5}\)
