Question

$\frac{1}{ \sqrt{2}+ \sqrt{3}+ \sqrt{5} }$ pode-se racionalizar

Answer 1

                   $\dfrac{1}{ \sqrt{2}+ \sqrt{3}+ \sqrt{5} }$

$F=\dfrac{1}{ \sqrt{2}+ \sqrt{3}+ \sqrt{5} } \cdot \dfrac{\sqrt{2}+ \sqrt{3}-\sqrt{5}}{\sqrt{2}+ \sqrt{3}-\sqrt{5}}\\ \\ \\ F=\dfrac{\sqrt{2}+ \sqrt{3}-\sqrt{5}}{ (\sqrt{2}+ \sqrt{3})^2-\sqrt{5}^2 } \\ \\ \\ F=\dfrac{\sqrt{2}+ \sqrt{3}-\sqrt{5}}{ 5+2\sqrt{6}-5} \\ \\ \\ F=\dfrac{\sqrt{2}+ \sqrt{3}-\sqrt{5}}{2\sqrt{6}} \\ \\ \\ \boxed{F=\dfrac{\sqrt{12}+ \sqrt{18}-\sqrt{30}}{12}}$