Question

Resolva:
$\frac{\sqrt{6}}{\sqrt{2+\sqrt{3}}}$

Answer 1

$\frac{\sqrt{6}}{\sqrt{2+\sqrt{3}}}=k\\\\(\frac{\sqrt{6}}{\sqrt{2+\sqrt{3}}})^2=(k)^2\\\\k^2=\frac{6}{2+\sqrt{3}}\\\\k^2=\frac{6}{2+\sqrt{3}}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\\\\k^2=\frac{6(2-\sqrt{3})}{4-3}\\\\k^2=6(2-\sqrt{3})\\\\\boxed{k=\sqrt{12-6\sqrt{3}}}$