Question

Racionalize a fração √2/√2+1
Como que faz?

Answer 1

$\mathsf{\dfrac{\sqrt{2}}{\sqrt{2}+1}}$

Multiplicando e divindo pelo conjugado do denominador temos

$\mathsf{\dfrac{\sqrt{2}}{(\sqrt{2}+1)}\dfrac{(\sqrt{2}-1)}{(\sqrt{2}-1)}}$

$\mathsf{\dfrac{\sqrt{2}(\sqrt{2}-1)}{{(\sqrt{2})}^{2}-{1}^{2}}}$

$\mathsf{\dfrac{\sqrt{2}(\sqrt{2}-1)}{2-1}=2-\sqrt{2}}$

$\huge\boxed{\boxed{\mathsf{\dfrac{\sqrt{2}}{\sqrt{2}+1}=2-\sqrt{2}}}}$