a) \(\sqrt{20}-\sqrt{45}-\sqrt{180}+3\sqrt{405}=\sqrt{4.5}-\sqrt{9.5}-\sqrt{36.5}+3.\sqrt{81.5}\)
\(=2\sqrt{5}-3\sqrt{5}-6\sqrt{5}+3.9\sqrt{5}=2\sqrt{5}-3\sqrt{5}-6\sqrt{5}+27\sqrt{5}\)
\(=20\sqrt{5}\)
b) \(\left(\sqrt{6}-\sqrt{5}\right)^2+\sqrt{120}=6+5-2\sqrt{30}+\sqrt{4.30}\)
\(=11-2\sqrt{30}+2\sqrt{30}=11\)
c) \(\dfrac{1}{2}\sqrt{6}-\sqrt{\dfrac{3}{2}}+3\sqrt{\dfrac{2}{3}}=\dfrac{1}{2}\sqrt{6}-\sqrt{\dfrac{1}{4}.6}+\sqrt{9.\dfrac{2}{3}}\)
\(=\dfrac{1}{2}\sqrt{6}-\dfrac{1}{2}\sqrt{6}+\sqrt{6}=\sqrt{6}\)