Задача 41. Вычислите    \(\left( {\sqrt {2\dfrac{2}{3}} -\sqrt {16\dfrac{2}{3}} } \right):\sqrt {\dfrac{2}{{27}}} \)

Ответ

ОТВЕТ: -9.

Решение

\(\left( {\sqrt {2\dfrac{2}{3}} -\sqrt {16\dfrac{2}{3}} } \right):\sqrt {\dfrac{2}{{27}}}  = \left( {\sqrt {\dfrac{8}{3}} -\sqrt {\dfrac{{50}}{3}} } \right) \cdot \sqrt {\dfrac{{27}}{2}}  = \sqrt {\dfrac{8}{3}}  \cdot \sqrt {\dfrac{{27}}{2}} -\sqrt {\dfrac{{50}}{3}}  \cdot \sqrt {\dfrac{{27}}{2}}  = \)

\( = \sqrt {\dfrac{{8 \cdot 27}}{{3 \cdot 2}}} -\sqrt {\dfrac{{50 \cdot 27}}{{3 \cdot 2}}}  = \sqrt {4 \cdot 9} -\sqrt {25 \cdot 9}  = 2 \cdot 3-5 \cdot 3 = 6-15 = -9.\)

Ответ:  \(-9.\)