Question

Va rog,urgent!
Tema din poza si de comparat
$2 \sqrt{2} ........ \sqrt[3]{9}$
Coroana!​

Answer 1

$\text{Ex 1:}\\\\\sqrt[2]{2\sqrt[5]{2}}\cdot \sqrt[10]{4\sqrt[4]{2^5\cdot 8}} = \\ \\ = 2^{\frac{1}{2}\cdot (1+\frac{1}{5})}\cdot 2^{\frac{1}{10}\cdot \left[2+\frac{1}{4}(5+3)\right]} = \\ \\ =2^{\frac{3}{5}}\cdot 2^{\frac{2}{5}} = 2^{\frac{2}{5}+\frac{3}{5}} =\\ \\ = 2^{\frac{5}{5}} = \boxed{2}$

$\text{Ex 2:}\\\\2\sqrt{2}\quad\text{cu}\quad \sqrt[3]{9}\,\,\Big|^2\\ 4\cdot 2\quad \text{cu}\quad \sqrt[3]{9^2}\,\,\Big|^3 \\ \\ 64\cdot 4\quad >\quad 9^2 \\ \\ \Rightarrow \boxed{2\sqrt{2}>\sqrt[3]{9}}$