Обчисліть:
1) $\sqrt{4\frac{33}{64}\cdot4\frac{21}{25}};$
2) $\sqrt{3\frac{4}{5}}\cdot\sqrt{6\frac{11}{19}};$
3) $\sqrt{175}\cdot\sqrt{28};$
4) $\sqrt{{25}^3}.$
Розв'язок:
1) $\sqrt{4\frac{33}{64}\cdot4\frac{21}{25}}=\sqrt{\frac{289}{64}\cdot\frac{121}{25}}=$
$= \frac{17}{8}\cdot\frac{11}{5}=\frac{187}{40}=4\frac{27}{40};$
2) $\sqrt{3\frac{4}{5}}\cdot\sqrt{6\frac{11}{19}}=\sqrt{\frac{19}{5}\cdot\frac{125}{19}}=$
$= \sqrt{\frac{19\cdot125}{5\cdot19}}=\sqrt{25}=5;$
3) $ \sqrt{175}\cdot\sqrt{28}=\sqrt{175\cdot28}=$
$= \sqrt{25\cdot7\cdot4\cdot7}=\sqrt{25\cdot4\cdot49}=$
$= 5\cdot2\cdot7=70;$
4) $\sqrt{{25}^3}=\sqrt{{25}^2\cdot25}=$
$= 25\sqrt{25}=25\cdot5=125.$