№ 17.16 Алгебра = № 33.16 Математика
Обчисліть значення частки:
1. $\frac{\sqrt{50}}{\sqrt2};$
2. $\frac{\sqrt{2,7}}{\sqrt{0,3}};$
3. $\frac{\sqrt{160}}{\sqrt{2,5}};$
4. $\frac{\sqrt2}{\sqrt{72}};$
5. $\frac{\sqrt{12}}{\sqrt{27}};$
6. $\frac{\sqrt{0,18}}{\sqrt{1,28}}.$
Розв'язок:
1. $\frac{\sqrt{50}}{\sqrt2}=\sqrt{\frac{50}{2}}=\sqrt{25}=5;$
2. $\frac{\sqrt{2,7}}{\sqrt{0,3}}=\sqrt{\frac{2,7}{0,3}}=\sqrt{\frac{27}{3}}=$
$= \sqrt9=3;$
3. $\frac{\sqrt{160}}{\sqrt{2,5}}=\sqrt{\frac{160}{2,5}}=\sqrt{\frac{1600}{25}}=$
$= \sqrt{64}=8;$
4. $\frac{\sqrt2}{\sqrt{72}}=\sqrt{\frac{2}{72}}=\sqrt{\frac{1}{36}}=\frac{1}{6};$
5. $\frac{\sqrt{12}}{\sqrt{27}}=\sqrt{\frac{12}{27}}=\sqrt{\frac{4}{9}}=\frac{2}{3};$
6. $\frac{\sqrt{0,18}}{\sqrt{1,28}}=\sqrt{\frac{0,18}{1,28}}=\sqrt{\frac{18}{128}}=$
$= \sqrt{\frac{9}{64}}=\frac{3}{8}.$