Question

calculați media geometrica a numerelor
$\sqrt{45} si \sqrt{125}$

Answer 1

$\text{m.g.}(\sqrt{45},\sqrt{125}) =\sqrt{\sqrt{45}\cdot \sqrt{125}} =\\\\ = \sqrt{\sqrt{45\cdot 125}} =\sqrt{\sqrt{5\cdot 9\cdot 5\cdot 25}} = \sqrt{\sqrt{5^2\cdot 9\cdot 5^2}} = \\ \\ = \sqrt{\sqrt{5^4\cdot 3^2}} = \sqrt{5^2\cdot 3} = 5\sqrt3$