Question

radical din 3
-------------------------------------- = ?
radical din 3 - radical din 2

Answer 1

$\frac{\sqrt{3}}{\sqrt{3}-\sqrt{2}}$
Se rationalizeaza numitorul
$=\frac{\sqrt{3}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})} \\ \\ =\frac{\sqrt{3}\cdot\sqrt{3}+\sqrt{3}\cdot\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2} \\ \\ =\frac{3+\sqrt{6}}{3-2} \\ \\ =\frac{3+\sqrt{6}}{1}=3+\sqrt{6}$