374*. (3√\frac{5}{6} +3√\frac{3}{10} -4√\frac{6}{5})⋅√\frac{5}{6}.

374*. Упростим выражение:

$$ \left(3\sqrt{\frac{5}{6}} +3\sqrt{\frac{3}{10}} -4\sqrt{\frac{6}{5}}\right) \cdot \sqrt{\frac{5}{6}} = 3\sqrt{\frac{5}{6}} \cdot \sqrt{\frac{5}{6}} + 3\sqrt{\frac{3}{10}} \cdot \sqrt{\frac{5}{6}} - 4\sqrt{\frac{6}{5}} \cdot \sqrt{\frac{5}{6}} $$.

$$ = 3 \cdot \frac{5}{6} + 3\sqrt{\frac{3}{10} \cdot \frac{5}{6}} - 4 \cdot 1 = \frac{15}{6} + 3\sqrt{\frac{15}{60}} - 4 = \frac{5}{2} + 3\sqrt{\frac{1}{4}} - 4 = \frac{5}{2} + 3 \cdot \frac{1}{2} - 4 = \frac{5}{2} + \frac{3}{2} - 4 = \frac{8}{2} - 4 = 4 - 4 = 0 $$.

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