Question

Racionalizando o denominador de (valor na imagem)

Answer 1

$\frac{3}{ \sqrt{2}+ \sqrt{5}} = \frac{3}{ \sqrt{2}+ \sqrt{5}} \cdot \frac{ \sqrt{2}- \sqrt{5}}{ \sqrt{2}- \sqrt{5}} =\frac{ 3(\sqrt{2}- \sqrt{5})}{ (\sqrt{2})^2- (\sqrt{5})^2} =\frac{ 3(\sqrt{2}- \sqrt{5})}{2-5}=\frac{ 3(\sqrt{2}- \sqrt{5})}{-3}\\ \\=\frac{ 3(\sqrt{2}- \sqrt{5})}{-3}= -(\sqrt{2}- \sqrt{5})=-\sqrt{2}+ \sqrt{5}=\sqrt{5}- \sqrt{2}$