Question

racionalize o denominador das frações abaixo
1/√3
4/√2
2/3√3
√2/√3
​

Answer 1

Olá!

$a) \: \frac{1}{ \sqrt{3} } = \\ \\ \frac{1}{ \sqrt{3} } \cdot \frac{ \sqrt{3} }{ \sqrt{3} } = \\ \\ \frac{1 \sqrt{3} }{ \sqrt{9} } = \\ \\ \boxed{ \bf{ \frac{ \sqrt{3} }{3} } }$

$b) \: \frac{4}{ \sqrt{2} } = \\ \\ \frac{4}{ \sqrt{2} } \cdot \frac{ \sqrt{2} }{ \sqrt{2} } = \\ \\ \frac{4 \sqrt{2} }{ \sqrt{4} } = \\ \\ \frac{ {4}^{\color{red}{ \div 2}} \sqrt{2} }{ {2}^{\color{red}{ \div 2}} } = \\ \\ \boxed{ \bf{ 2 \sqrt{2} } }$

$c) \: \frac{2}{3 \sqrt{3} } = \\ \\ \frac{2}{3 \sqrt{3} } \cdot \frac{3 \sqrt{3} }{3 \sqrt{3} } = \\ \\ \frac{2 \cdot3 \sqrt{3} }{3 \sqrt{3} \cdot3 \sqrt{3} } = \\ \\ \frac{6 \sqrt{3} }{9 \sqrt{9} } = \\ \\ \frac{6 \sqrt{3} }{9 \cdot3} = \\ \\ \frac{ { 6}^{\color{red}{ \div 3}} \sqrt{3} }{ {27}^{\color{red}{ \div 3}} } = \\ \\ \boxed{ \bf{ \frac{2 \sqrt{3} }{9} } }$

$d) \:\frac{ \sqrt{2} }{ \sqrt{3} } = \\ \\ \frac{ \sqrt{2} }{ \sqrt{3} } \cdot \frac{ \sqrt{3} }{ \sqrt{3} } = \\ \\ \frac{ \sqrt{2 \cdot3} }{ \sqrt{3 \cdot3} } = \\ \\ \frac{ \sqrt{6} }{ \sqrt{9} } = \\ \\ \boxed{ \bf{ \frac{ \sqrt{6} }{3} } }$

Espero ter ajudado! :)