Question

resultado da racionalizaçao do denominador da expressao

1/3-raiz de 6

2/raiz de 5+raiz de 3

Answer 1

$\mathsf{ \dfrac{1}{3-\sqrt{6}}= \dfrac{1}{(3 - \sqrt{6}) } \dfrac{(3+\sqrt{6})}{(3+\sqrt{6})}}=\\\mathsf{ \dfrac{3+\sqrt{6}}{3^2-{(\sqrt{6})}^{2}}=\dfrac{3+\sqrt{6}}{9-6}}$

$\large\boxed{\boxed{\mathsf{\dfrac{3+\sqrt{6}}{3}}}}$

$\mathsf{\dfrac{2}{\sqrt{5}+\sqrt{3}}=\dfrac{2}{(\sqrt{5}+\sqrt{3})}.\dfrac{(\sqrt{5}-\sqrt{3})}{(\sqrt{5}-\sqrt{3})}}$

$\mathsf{\dfrac{2(\sqrt{5}-\sqrt{3})}{{(\sqrt{5})}^2-{(\sqrt{3})}^2}=\dfrac{2(\sqrt{5}-\sqrt{3})}{5-3}}\\\mathsf{\dfrac{2(\sqrt{5}-\sqrt{3})}{2}} = \large\boxed{\boxed{\mathsf{\sqrt{5}-\sqrt{3}}}}$