Question

4/ raiz de 2 - 6 racionalização

Answer 1

Acredito que a expressão seja:

$\mathsf{\dfrac{4}{\sqrt{2}-6}}$

Racionalizando:

$\mathsf{\dfrac{4}{\sqrt{2}-6}\cdot \dfrac{\sqrt{2}+6}{\sqrt{2}+6}=}\\\\\\\mathsf{\dfrac{4\sqrt{2}+24}{\left(\sqrt{2}\right)^2-\left(6\right)^2}=}\\\\\\\mathsf{\dfrac{4\sqrt{2}+24}{2-36}=}\\\\\\\mathsf{\dfrac{4\sqrt{2}+24}{-34}=}\\\\\\\mathsf{\dfrac{4\cdot \left(\sqrt{2}+6\right)}{-34}=}\\\\\\\mathsf{\dfrac{2\cdot \left(\sqrt{2}+6\right)}{-17}=}\\\\\\\boxed{\mathsf{-\dfrac{2\left(\sqrt{2}+6\right)}{17}}}\: \: \checkmark$