757 Вправа 757Алгебра 8 клас Бевз 2025 · § 15 · стор. 145

757. Обчисли значення виразу.

а) ${\displaystyle \sqrt{5\frac{2}{5}}\cdot \sqrt{6\frac{2}{3}}=}$${\displaystyle \sqrt{\frac{27}{5}\cdot \frac{20}{3}}=}$${\displaystyle \sqrt{\frac{9\cdot \cancel{3}\cdot 4\cdot \cancel{5}}{\cancel{5}\cdot \cancel{3}}}=}$${\displaystyle \sqrt{36}=}$${\displaystyle 6}$;

б) ${\displaystyle \sqrt{\frac{2}{5}}\cdot \sqrt{12}\cdot \sqrt{1\frac{1}{5}}=}$${\displaystyle \sqrt{\frac{2}{5}\cdot 12\cdot \frac{6}{5}}=}$${\displaystyle \sqrt{\frac{144}{25}}}$=

=${\displaystyle \frac{12}{5}=}$${\displaystyle 2\frac{2}{5}}$;

в) ${\displaystyle \sqrt{\frac{4}{15}}\cdot \sqrt{1\frac{7}{8}}\cdot \sqrt{2\frac{13}{18}}=}$${\displaystyle \sqrt{\frac{4}{15}\cdot \frac{15}{8}\cdot \frac{49}{18}}=}$${\displaystyle \sqrt{\frac{4\cdot \cancel{15}\cdot 49}{\cancel{15}\cdot 8\cdot 18}}}$=

=${\displaystyle \sqrt{\frac{196}{144}}=}$${\displaystyle \frac{14}{12}=}$${\displaystyle \frac{7}{6}=}$${\displaystyle 1\frac{1}{6}}$.