Question

Racionalize as seguintes radiações

Answer 1

Explicação passo-a-passo:

.

$a) \dfrac{5}{ \sqrt{3} }$

$\dfrac{5}{ \sqrt{3} } \times \dfrac{ \sqrt{3} }{ \sqrt{3} }$

$\dfrac{5 \sqrt{3} }{ \sqrt{3} \sqrt{3} }$

$\dfrac{5 \sqrt{3} }{ \sqrt{9} }$

$\dfrac{5 \sqrt{3} }{3}$

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$b) \dfrac{ \sqrt{5} }{ \sqrt{2} }$

$\dfrac{ \sqrt{5} }{ \sqrt{2} } \times \dfrac{ \sqrt{2} }{ \sqrt{2} }$

$\dfrac{ \sqrt{5} \sqrt{2} }{ \sqrt{2} \sqrt{2} }$

$\dfrac{ \sqrt{10} }{ \sqrt{4} }$

$\dfrac{ \sqrt{10} }{2}$

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$c) \dfrac{6}{2 \sqrt{3} }$

$\dfrac{3}{ \sqrt{3} }$

$\dfrac{3}{ \sqrt{3} } \times \dfrac{ \sqrt{3} }{ \sqrt{3} }$

$\dfrac{3 \sqrt{3} }{ \sqrt{3} \sqrt{3} }$

$\dfrac{3 \sqrt{3} }{ \sqrt{9} }$

$\dfrac{3 \sqrt{3} }{3}$

$\sqrt{3}$

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$d) \dfrac{7}{ \sqrt[3]{a} }$

$\dfrac{7}{ \sqrt[3]{a} } \times \dfrac{ \sqrt[3]{a {}^{2} } }{ \sqrt[3]{a {}^{2} } }$

$\dfrac{7 \sqrt[3]{a {}^{2} } }{ \sqrt[3]{a} \sqrt[3]{a {}^{2} } }$

$\dfrac{7 \sqrt[3]{a {}^{2} } }{ \sqrt[3]{a \times a {}^{2} } }$

$\dfrac{7 \sqrt[3]{a {}^{2} } }{ \sqrt[3]{a {}^{3} } }$

$\dfrac{7 \sqrt[3]{a {}^{2} } }{ \sqrt[3 \div 3]{a {}^{3 \div 3} } }$

$\dfrac{7 \sqrt[3]{a {}^{2} } }{a}$

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$e) \dfrac{2}{ \sqrt{3} + \sqrt{5} }$

$\dfrac{2}{ \sqrt{3} + \sqrt{5} } \times \dfrac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} - \sqrt{5} }$

$\dfrac{2( \sqrt{3} - \sqrt{5}) }{( \sqrt{3} + \sqrt{5} )( \sqrt{3} - \sqrt{5} ) }$

$\dfrac{2( \sqrt{3} - \sqrt{5} ) }{( \sqrt{3) {}^{2} } - ( \sqrt{5} ) {}^{2} }$

$\dfrac{2( \sqrt{3} - \sqrt{5} ) }{ \sqrt[2 \div 2]{3 {}^{2 \div 2} } - \sqrt[2 \div 2]{5 {}^{2 \div 5} } }$

$\dfrac{2( \sqrt{3} - \sqrt{5} )}{3 - 5}$

$\dfrac{2( \sqrt{3} - \sqrt{5} ) }{ - 2}$

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

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

Answer 2

$a) \frac{5}{\sqrt{3} }= \frac{5\sqrt{3} }{3} \\\\b)\frac{\sqrt{5} }{\sqrt{2} } =\frac{\sqrt{10} }{2} \\\\c)\frac{6}{2\sqrt{3} }=\frac{12\sqrt{3} }{12}=\sqrt{3} \\\\d)\frac{7}{\sqrt[3]{a} } =\frac{7.\sqrt[3]{a^2} }{\sqrt[3]{a^2.\sqrt[3]{a} } }=\frac{7\sqrt[3]{a^2} }{a} } \\\\e)\frac{2}{\sqrt{3}+\sqrt{5} } =\frac{2\sqrt{3}-2\sqrt{5} }{-2}=-\sqrt{3}+\sqrt{5}$