Question

Fuvest ( Racionalização)
$\sqrt{2}+ \sqrt{3}/ \sqrt{3}$

Answer 1

$\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{3}}\\ \\ =\dfrac{\left(\sqrt{2}+\sqrt{3} \right )\cdot \left\sqrt{3}}{\sqrt{3}\cdot \sqrt{3}}\\ \\ =\dfrac{\sqrt{2}\cdot \sqrt{3}+\left(\sqrt{3} \right )^{2}}{\left(\sqrt{3} \right )^{2}}\\ \\ =\dfrac{\sqrt{2\cdot 3}+3}{3}\\ \\ =\dfrac{\sqrt{6}+3}{3}\\ \\ =\dfrac{\sqrt{6}}{3}+\dfrac{3}{3}\\ \\ =\dfrac{\sqrt{6}}{3}+1$