\(\dfrac{1}{\sqrt{3-2\sqrt{2}}}+\dfrac{1}{\sqrt{5-2\sqrt{6}}}\)
\(=\dfrac{1}{\sqrt{\left(\sqrt{2}\right)^2-2\cdot\sqrt{2}\cdot1+1^2}}+\dfrac{1}{\sqrt{\left(\sqrt{3}\right)^2-2\cdot\sqrt{3}\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}}\)
\(=\dfrac{1}{\sqrt{\left(\sqrt{2}-1\right)^2}}+\dfrac{1}{\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}}\)
\(=\dfrac{1}{\left|\sqrt{2}-1\right|}+\dfrac{1}{\left|\sqrt{3}-\sqrt{2}\right|}\)
\(=\dfrac{1}{\sqrt{2}-1}+\dfrac{1}{\sqrt{3}-\sqrt{2}}\)
\(=\dfrac{\sqrt{2}+1}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}+\dfrac{\sqrt{3}+\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}\)
\(=\dfrac{\sqrt{2}+1}{\left(\sqrt{2}\right)^2-1}+\dfrac{\sqrt{3}+\sqrt{2}}{\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2}\)
\(=\sqrt{2}+1+\sqrt{3}+\sqrt{2}\)
\(=2\sqrt{2}+\sqrt{3}+1\)
