Question

Bài tập: Thực hiện phép tính

\(\left(\dfrac{1}{3}\sqrt{\dfrac{1}{2}}-\dfrac{2}{3}\sqrt{\dfrac{1}{3}}+\dfrac{2}{7}\sqrt{\dfrac{4}{5}}\right):\left(\dfrac{2}{7}\sqrt{\dfrac{1}{8}}\right)\)

Answer 1

\(=\left(\dfrac{1}{3}\cdot\dfrac{\sqrt{2}}{2}-\dfrac{2}{3\sqrt{3}}+\dfrac{4}{7\sqrt{5}}\right):\left(\dfrac{2}{7}\cdot\dfrac{1}{2\sqrt{2}}\right)\)

\(=\left(\dfrac{\sqrt{2}}{6}-\dfrac{2\sqrt{3}}{9}+\dfrac{4\sqrt{5}}{35}\right):\dfrac{1}{7\sqrt{2}}\)

\(=\left(\dfrac{3\sqrt{2}-4\sqrt{3}}{18}+\dfrac{4\sqrt{5}}{35}\right)\cdot7\sqrt{2}\)

\(=\dfrac{105\sqrt{2}-140\sqrt{3}+72\sqrt{5}}{35\cdot18}\cdot7\sqrt{2}\)

\(=\dfrac{\sqrt{2}\left(105\sqrt{2}-140\sqrt{3}+72\sqrt{5}\right)}{90}\)