a: \(\dfrac{\sqrt{3}}{\sqrt{75}}=\sqrt{\dfrac{3}{75}}=\sqrt{\dfrac{1}{25}}=\dfrac{1}{5}\)
b: \(\dfrac{\sqrt{444}}{\sqrt{111}}=\sqrt{\dfrac{444}{111}}=\sqrt{4}=2\)
c: \(\dfrac{\sqrt{72}}{\sqrt{2}}=\sqrt{\dfrac{72}{2}}=\sqrt{36}=6\)
d: \(\dfrac{5\sqrt{48}-3\sqrt{27}+2\sqrt{12}}{3}\)
\(=\dfrac{5\cdot4\sqrt{3}-3\cdot3\sqrt{3}+2\cdot2\sqrt{3}}{3}\)
\(=\dfrac{15\sqrt{3}}{3}=5\sqrt{3}\)
e: \(\dfrac{\sqrt{32}-\sqrt{50}+\sqrt{8}}{\sqrt{2}}=\dfrac{4\sqrt{2}-5\sqrt{2}+2\sqrt{2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{2}}{\sqrt{2}}=1\)
f: \(2\sqrt{\dfrac{16}{3}}-3\cdot\sqrt{\dfrac{1}{27}}-6\cdot\sqrt{\dfrac{4}{75}}\)
\(=2\cdot\dfrac{4}{\sqrt{3}}-3\cdot\dfrac{1}{3\sqrt{3}}-6\cdot\dfrac{2}{5\sqrt{3}}\)
\(=\dfrac{8}{\sqrt{3}}-\dfrac{1}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}=\dfrac{7}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}=\dfrac{35-12}{5\sqrt{3}}=\dfrac{23}{5\sqrt{3}}\)
\(=\dfrac{23\sqrt{3}}{15}\)
