Question

Racionalize o denominador de cada fração a seguir: 

a) $\frac{11}{ \sqrt[5]{ 4^{3} } }$

b) $\frac{1}{ \sqrt{2} + 1}$

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

Answer 1

Oi :)

$\frac{11}{ \sqrt[5]{4^3} }. \frac{ \sqrt[5]{4^2} }{ \sqrt[5]{4^2} } = \frac{11 \sqrt[5]{4^2} }{4}$

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$\frac{1}{ \sqrt{2}+1 } . \frac{ \sqrt{2}-1 }{ \sqrt{2}-1 } = \frac{ \sqrt{2} -1}{ (\sqrt{2})^2 -1^2} = \frac{ \sqrt{2}-1 }{2-1} = \frac{ \sqrt{2} -1}{1}= \sqrt{2} -1$

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$\frac{-3}{ \sqrt{2}+ \sqrt{3} } . \frac{\sqrt{2}- \sqrt{3} }{\sqrt{2}- \sqrt{3} } = \frac{-3(\sqrt{2}- \sqrt{3} )}{ (\sqrt{2})^2 - (\sqrt{3})^2 } = \frac{-3(\sqrt{2}- \sqrt{3} )}{2-3 }= \frac{-3(\sqrt{2}- \sqrt{3} )}{-1 }=3(\sqrt{2}- \sqrt{3} )$