Question

Racionalize
Ajuda por favooor!!!!

Answer 1

Explicação passo-a-passo:

a) $\dfrac{9}{4\sqrt{2}}=\dfrac{9\cdot\sqrt{2}}{4\sqrt{2}\cdot\sqrt{2}}=\dfrac{9\sqrt{2}}{4\cdot\sqrt{4}}=\dfrac{9\sqrt{2}}{4\cdot2}=\dfrac{9\sqrt{2}}{8}$

b) $\dfrac{6}{5\sqrt{3}}=\dfrac{6\cdot\sqrt{3}}{5\sqrt{3}\cdot\sqrt{3}}=\dfrac{6\sqrt{3}}{5\cdot\sqrt{9}}=\dfrac{6\sqrt{3}}{5\cdot3}=\dfrac{6\sqrt{3}}{15}=\dfrac{2\sqrt{3}}{5}$

c) $\dfrac{9}{9+\sqrt{5}}=\dfrac{9\cdot(9-\sqrt{5})}{(9+\sqrt{5})\cdot(9-\sqrt{5})}=\dfrac{81-9\sqrt{5}}{81-5}=\dfrac{81-9\sqrt{5}}{76}$

d) $\dfrac{13}{1-\sqrt{7}}=\dfrac{13\cdot(1+\sqrt{7})}{(1-\sqrt{7})\cdot(1+\sqrt{7})}=\dfrac{13+13\sqrt{7}}{1-7}=\dfrac{13+13\sqrt{7}}{-6}=\dfrac{-13-13\sqrt{7}}{6}$