Question

racionalize os denominadores
$\frac{2}{ \sqrt{3 - \sqrt{2} } }$
​

Answer 1

$\displaystyle \frac{2}{\sqrt{3-\sqrt{2}}} \\\\\\ \underline{\text{racionalizando}}: \\\\ \frac{2}{\sqrt{3-\sqrt2}}.\frac{\sqrt{3-\sqrt2}}{\sqrt{3-\sqrt2}} \\\\\\ \frac{2\sqrt{3-\sqrt 2}}{\sqrt{(3-\sqrt{2})^2}} \\\\\\ \frac{2\sqrt{3-\sqrt{2}}}{3-\sqrt{2}}$

Racionalizando novamente :

$\displaystyle \frac{2\sqrt{3-\sqrt{2}}}{(3-\sqrt2)}\frac{3+\sqrt{2}}{(3+\sqrt2)} \\\\\\ \frac{2(3+\sqrt2).\sqrt{3-\sqrt{2}}}{3^2-(\sqrt2)^2} \\\\\\ \frac{2(3+\sqrt2)\sqrt{3-\sqrt2}}{9-2 } \\\\\\ \huge\boxed{\frac{2(3+\sqrt2)\sqrt{3-\sqrt2}}{7}}\checkmark$