c) \(\dfrac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}+\sqrt[3]{64}=\dfrac{\sqrt{3}\left(\sqrt{2}-1\right)}{-\left(\sqrt{2}-1\right)}+4=4-\sqrt{3}\)
d) \(\dfrac{2-3\sqrt{2}}{\sqrt{2}}+\dfrac{6}{3+\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
\(=\sqrt{2}-3+\left(3-\sqrt{3}\right)+\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\sqrt{2}-\sqrt{3}+\sqrt{3}+1\)
\(=\sqrt{2}+1\)
e) \(\sqrt{2}\left(\sqrt{21}+3\right)\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{21}+3\right)\sqrt{10-2\sqrt{21}}\)
\(=\sqrt{3}\left(\sqrt{3}+\sqrt{7}\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)
\(=\sqrt{3}\left[\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\right]\)
\(=\sqrt{3}\left(7-3\right)=4\sqrt{3}\)
