Question

racionalize a fração
$\frac{2}{ \sqrt{3 - \sqrt{5} } }$
​

Answer 1

Resposta:

2/[√(3-√5) ]=2[√(3-√5) ]/{[√(3-√5) ]*[√(3-√5) ]}

= 2[√(3-√5) ]/(3-√5)

= 2[√(3-√5) ]*(3+√5)/[(3-√5)*(3+√5) ]

= 2√(3-√5) *(3+√5)/(3²-√5²)

= 2√(3-√5) *(3+√5)/(9-5)

= 2√(3-√5) *(3+√5)/4

= [√(3-√5)] *(3+√5)/2

Answer 2

$\frac{2}{\sqrt{3-\sqrt{5} }} =\frac{2}{\sqrt{3-\sqrt{5} }} \cdot\frac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}} =\frac{2\cdot\sqrt{3+\sqrt{5}}}{\sqrt{3^2-(\sqrt{5})^2}} =\frac{2\cdot\sqrt{3+\sqrt{5}}}{\sqrt{9-5}} =\frac{2\cdot\sqrt{3+\sqrt{5}}}{\sqrt{4}}} \\\\=\frac{2\cdot\sqrt{3+\sqrt{5}}}{2}} =\sqrt{3+\sqrt{5}}}$