Question

Racionalizar: 

$\frac{10}{\sqrt{18} +2 \sqrt{2} }$

Resolver a expressão:

$\sqrt{\frac{3}{5}} + \sqrt{\frac{5}{3}}$

Answer 1

Veja:
$\boxed{ \sqrt{18}= \sqrt{9.2} = \sqrt{9} \sqrt{2}=3 \sqrt{2} }$


$\boxed{\frac{10}{ \sqrt{18}+2 \sqrt{2} }=\frac{10}{3 \sqrt{2}+2 \sqrt{2} }=\frac{10}{5 \sqrt{2} }=\frac{2}{ \sqrt{2} }.\frac{ \sqrt{2} }{ \sqrt{2} }= \sqrt{2} }$

$\boxed{ \sqrt{ \frac{3}{5} }+ \sqrt{ \frac{5}{3} } =\frac{ \sqrt{3} }{ \sqrt{5} }+ \frac{ \sqrt{5} }{ \sqrt{3} }=\frac{3+5}{ \sqrt{15} } =\frac{8}{ \sqrt{15} }.\frac{ \sqrt{15} }{ \sqrt{15} }=\frac{8 \sqrt{15} }{15}}$