Question

racionalizando as expressoes abaixo obteremos quais os valores?
A- 2 - √5
√5 + 2

B- 12 √2
5 √3

Answer 1

a) 

$\dfrac{2-\sqrt{5}}{\sqrt{5} + 2} \\ \\ \\ \dfrac{(2-\sqrt{5}) . (\sqrt{5} + 2)}{(\sqrt{5} + 2);(\sqrt{5} + 2)} \\ \\ \\ \dfrac{-1}{(\sqrt{5} + 2)^2} \\ \\ \\ \dfrac{-1}{9 +4 \sqrt{5}} \\ \\\\ \\ Inverter \ a \ frac\~ao \\ \\=> -9 + 4\sqrt{5}$

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b) 

$\dfrac{12\sqrt{2}}{5\sqrt{3}} \\ \\ \\ \dfrac{(12\sqrt{2}). (5\sqrt{3})}{(5\sqrt{3}). (5\sqrt{3})} \\ \\ \\ \dfrac{60\sqrt{6}}{(5\sqrt{3})^2} \\ \\ \\ \dfrac{60\sqrt{6}}{25 . 3}\\ \\ \\ \dfrac{60\sqrt{6}}{75}\\ \\ \\ => \dfrac{4\sqrt{6}}{5}$