Question

racionalizar a fração 20 / raiz quadrada de 6 + 1

Answer 1

$\frac{20}{ \sqrt{6}+1} = \frac{20}{ \sqrt{6}+1} * \frac{\sqrt{6}-1}{ \sqrt{6}-1} = \frac{20*(\sqrt{6}-1)}{ (\sqrt{6})^2-(1)^2} = \frac{20*(\sqrt{6}-1)}{ 6-1} = \\ \\ \\ \frac{20*(\sqrt{6}-1)}{ 5} ={4(\sqrt{6}-1)} =\boxed{4\sqrt{6}-4}$