Question

Thực hiện phép tính :

\(E=\frac{2}{\sqrt{3}}+\frac{\sqrt{2}}{3}+\frac{2}{\sqrt{3}}.\sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}}\)

Giúp mk nha (giải tắt cũng đc nhưng đừng viết đáp án nha )

Answer 1

\(E=\frac{2}{\sqrt{3}}+\frac{\sqrt{2}}{3}+\frac{2}{\sqrt{3}}.\left(\frac{5}{12}-\frac{1}{\sqrt{6}}\right)\)

\(E=\frac{2}{\sqrt{3}}+\frac{\sqrt{2}}{3}+\frac{5\sqrt{6}-12}{18\sqrt{2}}\)

\(E=\frac{36\sqrt{2}}{18\sqrt{6}}+\frac{12\sqrt{3}}{18\sqrt{6}}+\frac{\left(5\sqrt{6}-12\right).\sqrt{3}}{18\sqrt{3}}\)

\(E=\frac{36\sqrt{2}+12\sqrt{3}+\left(5\sqrt{6}-12\right).\sqrt{3}}{18\sqrt{6}}\)

\(E=\frac{51\sqrt{2}}{18\sqrt{6}}\)

\(E=\frac{17\sqrt{2}}{6\sqrt{6}}\)

\(E=\frac{17\sqrt{2}}{2.3\sqrt{2}.\sqrt{3}}\)

\(E=\frac{17}{\sqrt{2}.3\sqrt{2}.\sqrt{3}}\)

\(E=\frac{17}{6\sqrt{3}}\)

\(E=\frac{17\sqrt{3}}{18}\)