Question

Racionlize.
me ajudem por favor, não to conseguindo responder...

Answer 1

Para racionalizar esses produtos basta usar o produto notável $(a+b)*(a-b)=a^2-b^2$

$b) \frac{2}{\sqrt{3}-\sqrt{2}} \\ \frac{2}{\sqrt{3}-\sqrt{2}} *\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}} \\\\ \frac{2(\sqrt{3}+\sqrt{2})}{9-5}\\ \frac{(\sqrt{3}+\sqrt{2})}{2} }\\\\\\ c) \ \frac{2}{2+\sqrt{3}} \\ \frac{2}{2+\sqrt{3}} *\frac{2-\sqrt{3}}{2-\sqrt{3}} \\\\ \frac{2(2-\sqrt{3})}{4-3}\\ 2(2-\sqrt{3})\\\\ d) \ \frac{5}{3+\sqrt{2}} \\ \frac{5}{3+\sqrt{2}}* \frac{3-\sqrt{2}}{3-\sqrt{2}}\\ \frac{5(3-\sqrt{2})}{9-2}\\ \frac {5(3- \sqrt{2})}{7}$
$e) \ \frac{7}{\sqrt{7}-\sqrt{2}} \\ \frac{7}{\sqrt{7}-\sqrt{2}} *\frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}+\sqrt{2}} \\\\ \frac{7(\sqrt{7}+\sqrt{2})}{7-2}\\ \frac{7(\sqrt{7}+\sqrt{2})}{5} }\\\\\\ f) \ \frac{5}{\sqrt{5}-\sqrt{2}} \\ \frac{5}{\sqrt{5}-\sqrt{2}} *\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}} \\\\ \frac{5(\sqrt{5}+\sqrt{2})}{5-2}\\ \frac{5(\sqrt{5}+\sqrt{2})}{3} }$