732 Вправа 732Алгебра 8 клас Бевз 2025 · § 15 · стор. 143

732. Обчисли значення виразу.

а) ${\displaystyle \sqrt{4\cdot 9\cdot 25}=}$${\displaystyle \sqrt{4}\cdot \sqrt{9}\cdot \sqrt{25}=}$${\displaystyle 2\cdot 3\cdot 5=}$${\displaystyle 30}$;

б) ${\displaystyle \sqrt{36\cdot 225\cdot 144}=}$${\displaystyle \sqrt{36}\cdot \sqrt{225}\cdot \sqrt{144}}$=

=${\displaystyle 6\cdot 15\cdot 12=}$${\displaystyle 1080}$;

в) ${\displaystyle \sqrt{144\cdot 36\cdot 25\cdot 9}=}$${\displaystyle \sqrt{144}\cdot \sqrt{36}\cdot \sqrt{25}\cdot \sqrt{9}}$=

=${\displaystyle 12\cdot 6\cdot 5\cdot 3=}$${\displaystyle 1080}$;

г) ${\displaystyle \sqrt{5\frac{1}{16}\cdot 9}=}$${\displaystyle \sqrt{\frac{81}{16}\cdot 9}=}$${\displaystyle \sqrt{\frac{81}{16}}\cdot \sqrt{9}=}$${\displaystyle \frac{9}{4}\cdot 3}$=

=${\displaystyle \frac{27}{4}=}$${\displaystyle 6\frac{3}{4}}$;

ґ) ${\displaystyle \sqrt{12\frac{1}{4}\cdot 10\frac{6}{25}}=}$${\displaystyle \sqrt{\frac{49}{4}\cdot \frac{256}{25}}=}$${\displaystyle \frac{7}{2}\cdot \frac{16}{5}=}$${\displaystyle \frac{7\cdot \cancel{2}\cdot 8}{\cancel{2}\cdot 5}}$=

=${\displaystyle \frac{56}{5}=}$${\displaystyle 11\frac{1}{5}}$;

д) ${\displaystyle \sqrt{\frac{16}{25}\cdot \frac{49}{36}\cdot \frac{64}{81}}=}$${\displaystyle \frac{4}{5}\cdot \frac{7}{6}\cdot \frac{8}{9}=}$${\displaystyle \frac{\cancel{2}\cdot 2\cdot 7\cdot 8}{5\cdot \cancel{2}\cdot 3\cdot 9}=}$${\displaystyle \frac{112}{135}}$.