Реши задание на изображении

Краткие ответы

5. \(-2\)

6. \(15\sqrt[3]{5}+120\sqrt[4]{2}-4\)

7. \(-60\sqrt[4]{2}-0{,}1\)

8. \(35\)

9. \(-0{,}2\)

10. \(20+180\sqrt[4]{2}\)

11. \(3-5\sqrt[3]{6}\)

12. \(\dfrac{\sqrt[3]{90}-\sqrt[3]{30}}{2}\)

Ключевые шаги

5

\[ \sqrt[3]{(-5)^2}\cdot\sqrt[3]{-5} =\sqrt[3]{25\cdot(-5)} =\sqrt[3]{-125}=-5. \]

\[ \frac{\sqrt[3]{297}\cdot\sqrt4}{\sqrt[3]{88}} = 2\sqrt[3]{\frac{27\cdot11}{8\cdot11}} = 2\sqrt[3]{\frac{27}{8}} =2\cdot\frac32=3. \]

\[ -5+3=-2. \]

6

\[ \sqrt[3]{135}\cdot\sqrt{25}-\sqrt{16} =3\sqrt[3]{5}\cdot5-4 =15\sqrt[3]{5}-4. \]

\[ \sqrt[4]{128}\cdot\sqrt[3]{125}\cdot\sqrt{72} = (2\sqrt[4]{8})\cdot5\cdot6\sqrt2 =120\sqrt[4]{2}. \]

Итак,

\[ 15\sqrt[3]{5}+120\sqrt[4]{2}-4. \]

7

\[ \sqrt[4]{128}\cdot\sqrt[3]{-125}\cdot\sqrt{18} = (2\sqrt[4]{8})(-5)(3\sqrt2) =-60\sqrt[4]{2}. \]

\[ \sqrt[3]{-0{,}001}=-0{,}1. \]

Ответ:

\[ -60\sqrt[4]{2}-0{,}1. \]

8

\[ \sqrt{(-5)^2\cdot3^2} =\sqrt{25\cdot9}=15. \]

\[ \sqrt[3]{-81}\cdot\sqrt[3]{-9} =\sqrt[3]{729}=9. \]

\[ 15+9+\sqrt{121}=15+9+11=35. \]

9

\[ \sqrt[3]{-0{,}2}\cdot\sqrt[3]{0{,}04} = \sqrt[3]{-0{,}008} =-0{,}2, \]

так как \((-0{,}2)^3=-0{,}008\).

10

\[ \sqrt[3]{81}\cdot\sqrt[3]{9} =\sqrt[3]{729}=9, \qquad \sqrt{121}=11. \]

\[ \sqrt[4]{128}\cdot\sqrt[3]{125}\cdot\sqrt{162} = (2\sqrt[4]{8})\cdot5\cdot9\sqrt2 =180\sqrt[4]{2}. \]

\[ 9+11+180\sqrt[4]{2} =20+180\sqrt[4]{2}. \]

11

\[ \frac{\sqrt[3]{297}\cdot\sqrt4}{\sqrt[3]{88}} = 2\sqrt[3]{\frac{27\cdot11}{8\cdot11}} =3. \]

\[ \sqrt[3]{6\cdot(-5)^3} =\sqrt[3]{-750} =-5\sqrt[3]{6}. \]

\[ 3-5\sqrt[3]{6}. \]

12

\[ \frac{\sqrt[3]{900}-\sqrt[3]{300}}{\sqrt[3]{80}} = \sqrt[3]{\frac{900}{80}}-\sqrt[3]{\frac{300}{80}} = \sqrt[3]{\frac{45}{4}}-\sqrt[3]{\frac{15}{4}}. \]

\[ \sqrt[3]{\frac{45}{4}}=\frac{\sqrt[3]{90}}2, \qquad \sqrt[3]{\frac{15}{4}}=\frac{\sqrt[3]{30}}2. \]

Поэтому

\[ \boxed{\frac{\sqrt[3]{90}-\sqrt[3]{30}}2}. \]