Question

Racionalize:

$\frac{3}{\sqrt{2}+3 }$

Answer 1

     $\frac{3}{\sqrt{2}+3}\\ \\ para~racionalizar, como~existe~um\\numero~adiconando~ao~denominador,\\multiplicamos~ambos~pelo~inveso.\\ \\ \frac{3}{\sqrt{2}+3}\times\frac{\sqrt{2}-3}{\sqrt{2}-3}=\dfrac{3\left(\sqrt2-3 \right)}{\sqrt4-3^2}=\dfrac{3\sqrt2-\backslash\!\!\!9 \ri}{2+\backslash\!\!\!9}=\\\\ \dfrac{3\sqrt2}{2}\\\\\\ \boxed{\begin{array}{lr}\dfac{3\sqrt2}[2}\end{array}}$

resposta:${\dfrac{3\sqrt2}{2}}$