Kết quả phép tính ​\(\begin{aligned} &\frac{1}{\sqrt{3}}+\frac{1}{3 \sqrt{2}}+\frac{1}{\sqrt{3}} \sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}} \end{aligned}\) là:

* Hướng dẫn giải

Ta có:

 \(\begin{aligned} &\frac{1}{\sqrt{3}}+\frac{1}{3 \sqrt{2}}+\frac{1}{\sqrt{3}} \sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}} \\ &=\frac{\sqrt{3}}{3}+\frac{\sqrt{2}}{6}+\frac{\sqrt{3}}{3} \cdot \sqrt{\frac{5-2 \sqrt{6}}{12}}=\frac{\sqrt{3}}{3}+\frac{\sqrt{2}}{6}+\frac{\sqrt{3}}{3} \cdot \sqrt{\frac{\sqrt{3}-\sqrt{2}^{2}}{12}} \\ &=\frac{\sqrt{3}}{3}+\frac{\sqrt{2}}{6}+\frac{\sqrt{3}}{3} \cdot \frac{\sqrt{3}-\sqrt{2}}{2 \sqrt{3}}=\frac{\sqrt{3}}{3}+\frac{\sqrt{2}}{6}+\frac{\sqrt{3}-\sqrt{2}}{6}=\frac{3 \sqrt{3}}{6}=\frac{\sqrt{3}}{2} \end{aligned}\)