Question

arătați că √(2√2(√2√2)) aparține intervalului (1;2)​

Answer 1

$\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}} \in (1;2) \Rightarrow 1 < \sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}< 2\Big|^2 \Rightarrow$

$\Rightarrow 1 < 2\sqrt{2\sqrt{2\sqrt{2}}}<4 \Big|^2 \Rightarrow 1 < 4\cdot 2\sqrt{2\sqrt{2}}<16 \Big|^2 \Rightarrow$

$\Rightarrow 1 < 16\cdot 4\cdot 2\sqrt{2}< 256\Big|^2 \Rightarrow 1 < 256\cdot 16\cdot 4\cdot 2 < 256^2 \Rightarrow$

$\Rightarrow 1 < 256\cdot 128 < 256\cdot 256\,\,\,(A)$