Обчисліть:
1) $\sqrt{9\frac{49}{64}\cdot6\frac{3}{121}};$
2) $\sqrt{4\frac{1}{4}}\cdot\sqrt{3\frac{13}{17}};$
3) $\sqrt{80}\cdot\sqrt{605};$
4) $\sqrt{{36}^3}.$
Розв'язок:
1) $\sqrt{9\frac{49}{64}\cdot6\frac{3}{121}}=\sqrt{\frac{625}{64}\cdot\frac{729}{121}}=$
$= \frac{\sqrt{625}}{\sqrt{64}}\cdot\frac{\sqrt{729}}{\sqrt{121}}=\frac{25}{8}\cdot\frac{27}{11}=$
$= \frac{675}{88}=7\frac{59}{88};$
2) $\sqrt{4\frac{1}{4}}\cdot\sqrt{3\frac{13}{17}}=\sqrt{\frac{17}{4}\cdot\frac{64}{17}}=$
$= \sqrt{\frac{17\cdot64}{4\cdot17}}=\sqrt{16}=4;$
3) $ \sqrt{80}\cdot\sqrt{605}=\sqrt{80\cdot605}=$
$= \sqrt{16\cdot5\cdot121\cdot5}=$
$= \sqrt{16\cdot121\cdot25}=$
$= 4\cdot11\cdot5=220;$
4) $\sqrt{{36}^3}=\sqrt{{36}^2\cdot36}=$
$= 36\sqrt{36}= 36\cdot6=216.$