Question

Racionalize o denominador de cada expressão a seguir:

Answer 1

a) $\frac{1}{3-\sqrt{6} }=$

$\frac{1}{3-\sqrt{6} }\cdot \frac{3+\sqrt{6} }{3+\sqrt{6} }=$

$\frac{3+\sqrt{6} }{9-6}=$

$\frac{3+\sqrt{6} }{3}$

b) $\frac{2}{\sqrt{5}+\sqrt{3} }=$

$\frac{2}{\sqrt{5}+\sqrt{3} }\cdot \frac{\sqrt{5}-\sqrt{3} }{\sqrt{5}-\sqrt{3} }=$

$\frac{2(\sqrt{5}-\sqrt{3})}{5-3}=$

$\frac{2(\sqrt{5}-\sqrt{3}) }{2}=$

$\sqrt{5}-\sqrt{3}$

c) $\frac{2-\sqrt{2} }{3+\sqrt{2} }=$

$\frac{2-\sqrt{2} }{3+\sqrt{2} } \cdot \frac{3-\sqrt{2} }{3-\sqrt{2} }=$

$\frac{6-2\sqrt{2}-3\sqrt{2}+2 }{9-2}=$

$\frac{8-5\sqrt{2} }{7}$

d) $\frac{\sqrt{3}-\sqrt{2} }{\sqrt{3}+\sqrt{2} } =$

$\frac{\sqrt{3}-\sqrt{2} }{\sqrt{3}+\sqrt{2} } \cdot \frac{\sqrt{3}-\sqrt{2} }{\sqrt{3}-\sqrt{2} }=$

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

$\frac{5-2\sqrt{6} }{1}=$

$5-2\sqrt{6}$