558 Вправа 558Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 162

558. Знайдіть значення виразу:

1) ${\displaystyle \sqrt{0,11}\cdot \sqrt{\frac{1}{44}}+\sqrt{1,8}\cdot \sqrt{20}}$;

${\displaystyle \sqrt{0,11}\cdot \sqrt{\frac{1}{44}}=}$${\displaystyle \sqrt{\frac{11}{100}\cdot \frac{1}{44}}=}$${\displaystyle \sqrt{\frac{1}{100\cdot 4}}=}$${\displaystyle \sqrt{\frac{1}{400}}=}$${\displaystyle \frac{1}{20}=}$${\displaystyle 0,05}$;

${\displaystyle \sqrt{1,8}\cdot \sqrt{20}=}$${\displaystyle \sqrt{1,8\cdot 20}=}$${\displaystyle \sqrt{36}=}$${\displaystyle 6}$;

${\displaystyle 0,05+6=}$${\displaystyle 6,05}$;

2) ${\displaystyle \sqrt{0}:\sqrt{5\frac{1}{3}}\cdot \sqrt{3,84}=}$${\displaystyle 0:\sqrt{5\frac{1}{3}}\cdot \sqrt{3,84}=}$${\displaystyle 0}$;

3) ${\displaystyle 3\frac{4}{15}=}$${\displaystyle \frac{49}{15}}$; ${\displaystyle 0,75=}$${\displaystyle \frac{3}{4}}$; ${\displaystyle 1\frac{4}{5}=}$${\displaystyle \frac{9}{5}}$;

${\displaystyle \sqrt{\frac{49}{15}\cdot \frac{3}{4}\cdot \frac{9}{5}}=}$${\displaystyle \sqrt{\frac{49\cdot 3\cdot 9}{15\cdot 4\cdot 5}}=}$${\displaystyle \sqrt{\frac{49\cdot 9}{25\cdot 4}}=}$${\displaystyle \frac{7\cdot 3}{5\cdot 2}=}$${\displaystyle \frac{21}{10}=}$${\displaystyle 2,1}$;

4) ${\displaystyle \frac{\sqrt{200}}{\sqrt{0,02}}+\frac{\sqrt{0,9}}{\sqrt{1,6}}}$;

${\displaystyle \frac{\sqrt{200}}{\sqrt{0,02}}=}$${\displaystyle \sqrt{\frac{200}{0,02}}=}$${\displaystyle \sqrt{10000}=}$${\displaystyle 100}$;

${\displaystyle \frac{\sqrt{0,9}}{\sqrt{1,6}}=}$${\displaystyle \sqrt{\frac{9}{16}}=}$${\displaystyle \frac{3}{4}=}$${\displaystyle 0,75}$;

${\displaystyle 100+0,75=}$${\displaystyle 100,75}$.