Question

Racionalize os denominadores de cada uma das seguintes frações:
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Answer 1

Explicação passo-a-passo:

A

$\dfrac{1}{ \sqrt{2} }$

$\dfrac{1}{ \sqrt{2} } \times \dfrac{ \sqrt{2} }{ \sqrt{2} }$

$\dfrac{1 \sqrt{2} }{ \sqrt{2} \sqrt{2} }$

$\dfrac{1 \sqrt{2} }{ \sqrt{4} }$

$\dfrac{1 \sqrt{2} }{2}$

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

B

$\dfrac{6}{ \sqrt{3} }$

$\dfrac{6}{ \sqrt{3} } \times \dfrac{ \sqrt{3} }{ \sqrt{3} }$

$\dfrac{6 \sqrt{3} }{ \sqrt{3} \sqrt{3} }$

$\dfrac{6 \sqrt{3} }{ \sqrt{9} }$

$\dfrac{6 \sqrt{3} }{3}$

$2 \sqrt{3}$

C

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

$\dfrac{1}{ \sqrt{2} }$

$\dfrac{1}{ \sqrt{2} } \times \dfrac{ \sqrt{2} }{ \sqrt{2} }$

$\dfrac{1 \sqrt{2} }{ \sqrt{2} \sqrt{2} }$

$\dfrac{1 \sqrt{2} }{ \sqrt{4} }$

$\dfrac{1 \sqrt{2} }{2}$

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

D

$\dfrac{7}{10 \sqrt{5} }$

$\dfrac{7}{10 \sqrt{5} } \times \dfrac{ \sqrt{5} }{ \sqrt{5} }$

$\dfrac{7 \sqrt{5} }{10 \sqrt{5} \sqrt{5} }$

$\dfrac{7 \sqrt{5} }{10 \sqrt{25} }$

$\dfrac{7 \sqrt{5} }{10 \times 5}$

$\dfrac{7 \sqrt{5} }{50}$

E

$\sqrt{ \dfrac{9}{15} }$

$\sqrt{ \dfrac{9 {}^{ \div 3} }{15 {}^{ \div 3} } }$

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

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

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

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

$\dfrac{ \sqrt{15} }{ \sqrt{25} }$

$\dfrac{ \sqrt{15} }{5}$

F

$\dfrac{4 + \sqrt{2} }{ \sqrt{5} }$

$\dfrac{4 + \sqrt{2} }{ \sqrt{5} } \times \dfrac{ \sqrt{5} }{ \sqrt{5} }$

$\dfrac{(4 + \sqrt{2}) \sqrt{5} }{ \sqrt{5} \sqrt{5} }$

$\dfrac{4 \sqrt{5} + \sqrt{2} \sqrt{5} }{ \sqrt{25} }$

$\dfrac{4 \sqrt{5} + \sqrt{10} }{5}$

G

$\dfrac{5}{ \sqrt[3]{2} }$

$\dfrac{5}{ \sqrt[3]{2} } \times \dfrac{ \sqrt[3]{2 {}^{2} } }{ \sqrt[3]{2 {}^{2} } }$

$\dfrac{5 \sqrt[3]{2 {}^{2} } }{ \sqrt[3]{2 {}^{3} } \sqrt[3]{2 {}^{2} } }$

$\dfrac{5 \sqrt[3]{4} }{ \sqrt[3]{2 \times 2 {}^{2} } }$

$\dfrac{5 \sqrt[3]{4} }{ \sqrt[3]{2 {}^{3} } }$

$\dfrac{5 \sqrt[3]{4} }{2}$

H

$\dfrac{5}{ \sqrt{7} \sqrt{2} }$

$\dfrac{5}{ \sqrt{14} }$

$\dfrac{5}{ \sqrt{14} } \times \dfrac{ \sqrt{14} }{ \sqrt{14} }$

$\dfrac{5 \sqrt{14} }{ \sqrt{14} \sqrt{14} }$

$\dfrac{5 \sqrt{14} }{ \sqrt{196} }$

$\dfrac{5 \sqrt{14} }{14}$