a: \(7\sqrt{2}+\sqrt{8}-\sqrt{32}\)
\(=7\sqrt{2}+2\sqrt{2}-4\sqrt{2}\)
\(=5\sqrt{2}\)
b: \(2\sqrt{5}-\sqrt{\left(2-\sqrt{5}\right)^2}\)
\(=2\sqrt{5}-\left|2-\sqrt{5}\right|\)
\(=2\sqrt{5}-\left(\sqrt{5}-2\right)\)
\(=2\sqrt{5}-\sqrt{5}+2=\sqrt{5}+2\)
c: \(\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right)\cdot\dfrac{\sqrt{5}-1}{5-\sqrt{5}}\)
\(=\dfrac{3+\sqrt{5}-\left(3-\sqrt{5}\right)}{9-5}\cdot\dfrac{\sqrt{5}-1}{\sqrt{5}\left(\sqrt{5}-1\right)}\)
\(=\dfrac{3+\sqrt{5}-3+\sqrt{5}}{4}\cdot\dfrac{1}{\sqrt{5}}=\dfrac{2\sqrt{5}}{4\sqrt{5}}=\dfrac{1}{2}\)
d: \(\dfrac{10\sqrt{18}+5\sqrt{3}-15\sqrt{27}}{3\sqrt{2}-4\sqrt{3}}\)
\(=\dfrac{10\cdot3\sqrt{2}+5\sqrt{3}-15\cdot3\sqrt{3}}{3\sqrt{2}-4\sqrt{3}}\)
\(=\dfrac{30\sqrt{2}-40\sqrt{3}}{3\sqrt{2}-4\sqrt{3}}=\dfrac{10\left(3\sqrt{2}-4\sqrt{3}\right)}{3\sqrt{2}-4\sqrt{3}}=10\)
