a) \(\sqrt{27}-2\sqrt{12}-\sqrt{75}\)
\(=\sqrt{3^2\cdot3}-2\cdot2\sqrt{3}-\sqrt{5^2\cdot3}\)
\(=3\sqrt{3}-4\sqrt{3}-5\sqrt{3}\)
\(=-6\sqrt{3}\)
b) \(\dfrac{4}{3-\sqrt{5}}+\dfrac{3+2\sqrt{3}}{\sqrt{3}}-\left(\sqrt{3}+\sqrt{5}\right)\)
\(=\dfrac{4\left(3+\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}+\dfrac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}-\left(\sqrt{3}+\sqrt{5}\right)\)
\(=\dfrac{4\left(3+\sqrt{5}\right)}{4}+\sqrt{3}+2-\sqrt{3}-\sqrt{5}\)
\(=3+\sqrt{5}+\sqrt{3}+2-\sqrt{3}-\sqrt{5}\)
\(=5\)
c) \(\sqrt{7+4\sqrt{3}}+\sqrt{\left(2-\sqrt{3}\right)^2}\)
\(=\sqrt{2^2+2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}+\left|2-\sqrt{3}\right|\)
\(=\sqrt{\left(2+\sqrt{3}\right)^2}+2-\sqrt{3}\)
\(=\left|2+\sqrt{3}\right|+2-\sqrt{3}\)
\(=2+\sqrt{3}+2-\sqrt{3}\)
\(=4\)
