a) \(\left(\sqrt{45}-\sqrt{20}+\sqrt{5}\right):\sqrt{6}\)
\(=\left(3\sqrt{5}-2\sqrt{5}+\sqrt{5}\right):\sqrt{6}\)
\(=2\sqrt{5}:\sqrt{6}\)
\(=\sqrt{\dfrac{20}{6}}\)
\(=\sqrt{\dfrac{10}{3}}\)
\(=\dfrac{\sqrt{30}}{3}\)
b) \(\left(\sqrt{\dfrac{1}{7}}-\sqrt{\dfrac{16}{7}}+\sqrt{7}\right):\sqrt{7}\)
\(=\left(\sqrt{\dfrac{1}{7}}-4\sqrt{\dfrac{1}{7}}+\sqrt{7}\right):\sqrt{7}\)
\(=\left(-3\sqrt{\dfrac{1}{7}}+\sqrt{7}\right):\sqrt{7}\)
\(=4\sqrt{\dfrac{1}{7}}:\sqrt{7}\)
\(=\dfrac{4}{7}\)
c) \(\left(\sqrt{325}-\sqrt{117}+2\sqrt{208}\right):\sqrt{13}\)
\(=\left(5\sqrt{13}-3\sqrt{13}+8\sqrt{13}\right):\sqrt{13}\)
\(=10\sqrt{13}:\sqrt{13}\)
\(=10\)
d) \(\left(\dfrac{1}{3}\sqrt{\dfrac{1}{2}}-\dfrac{2}{3}\sqrt{\dfrac{3}{2}}+\dfrac{2}{7}\sqrt{\dfrac{1}{6}}\right):\left(\dfrac{2}{7}\sqrt{\dfrac{1}{8}}\right)\)
\(=\left(\dfrac{\sqrt{2}}{6}-\dfrac{\sqrt{6}}{3}+\dfrac{\sqrt{6}}{21}\right):\dfrac{\sqrt{2}}{14}\)
\(=\dfrac{-12\sqrt{6}+7\sqrt{2}}{42}:\dfrac{\sqrt{2}}{14}\)
\(=\dfrac{7-12\sqrt{3}}{3}\)
