549 Вправа 549Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 160

549. Обчисліть:

1) ${\displaystyle \sqrt{2\frac{7}{9}}=}$${\displaystyle \sqrt{\frac{25}{9}}=}$${\displaystyle \frac{\sqrt{25}}{\sqrt{9}}=}$${\displaystyle \frac{5}{3}=}$${\displaystyle 1\frac{2}{3}}$;

2) ${\displaystyle \sqrt{1\frac{9}{16}}=}$${\displaystyle \sqrt{\frac{25}{16}}=}$${\displaystyle \frac{\sqrt{25}}{\sqrt{16}}=}$${\displaystyle \frac{5}{4}=}$${\displaystyle 1\frac{1}{4}}$;

3) ${\displaystyle \sqrt{4\frac{21}{25}}=}$${\displaystyle \sqrt{\frac{121}{25}}=}$${\displaystyle \frac{\sqrt{121}}{\sqrt{25}}=}$${\displaystyle \frac{11}{5}=}$${\displaystyle 2\frac{1}{5}}$;

4) ${\displaystyle \sqrt{1\frac{13}{36}}=}$${\displaystyle \sqrt{\frac{49}{36}}=}$${\displaystyle \frac{\sqrt{49}}{\sqrt{36}}=}$${\displaystyle \frac{7}{6}=}$${\displaystyle 1\frac{1}{6}}$;

5) ${\displaystyle \sqrt{2\frac{1}{4}}=}$${\displaystyle \sqrt{\frac{9}{4}}=}$${\displaystyle \frac{\sqrt{9}}{\sqrt{4}}=}$${\displaystyle \frac{3}{2}=}$${\displaystyle 1\frac{1}{2}}$;

6) ${\displaystyle \sqrt{1\frac{19}{81}}=}$${\displaystyle \sqrt{\frac{100}{81}}=}$${\displaystyle \frac{\sqrt{100}}{\sqrt{81}}=}$${\displaystyle \frac{10}{9}=}$${\displaystyle 1\frac{1}{9}}$;

7) ${\displaystyle \sqrt{6\frac{1}{4}}=}$${\displaystyle \sqrt{\frac{25}{4}}=}$${\displaystyle \frac{\sqrt{25}}{\sqrt{4}}=}$${\displaystyle \frac{5}{2}=}$${\displaystyle 2\frac{1}{2}}$;

8) ${\displaystyle \sqrt{3\frac{1}{16}}=}$${\displaystyle \sqrt{\frac{49}{16}}=}$${\displaystyle \frac{\sqrt{49}}{\sqrt{16}}=}$${\displaystyle \frac{7}{4}=}$${\displaystyle 1\frac{3}{4}}$.