Упростите: корень из (2/5)+корень из 5/2+корень из 10.

\[\sqrt{\frac{2}{5}} + \sqrt{\frac{5}{2}} + \sqrt{10} =\]

\[= \frac{{\sqrt{2}}^{\backslash\text{√}2}}{\sqrt{5}} + \frac{{\sqrt{5}}^{\text{√}5}}{\sqrt{2}} + {\sqrt{10}}^{\backslash\text{√}10} =\]

\[= \frac{4 + 5 + 10}{\sqrt{5} \cdot \sqrt{2}} = \frac{19}{\sqrt{10}} =\]

\[= \frac{19\sqrt{10}}{10} = 1,9\sqrt{10}.\]