Thực hiện phép tính
a. 2\(\sqrt{\dfrac{16}{3}}\) - 3\(\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
b. \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\)
c.\(2\sqrt{27}-6\sqrt{\dfrac{4}{3}}+\dfrac{3}{5}\sqrt{75}\)
d. \(\dfrac{1}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
e. \(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
d. \(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
e. \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
g. \(\sqrt{4-\sqrt{9}+4\sqrt{2}}\)
a: \(=2\cdot\dfrac{4}{3}\sqrt{3}-3\cdot\dfrac{1}{9}\sqrt{3}-6\cdot\dfrac{2}{15}\sqrt{3}\)
\(=\dfrac{8}{3}\sqrt{3}-\dfrac{1}{3}\sqrt{3}-\dfrac{4}{5}\sqrt{3}=\dfrac{23}{15}\sqrt{3}\)
b: \(=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(2+\sqrt{3}\right)^2}\)
\(=2-\sqrt{3}+2+\sqrt{3}=4\)
c: \(=6\sqrt{3}-4\sqrt{3}+\dfrac{3}{5}\cdot5\sqrt{3}=2\sqrt{3}+3\sqrt{3}=5\sqrt{3}\)
