Question

Calcule os quocientes a seguir.
A)
$\sqrt[3]{40} \div \sqrt[3]{5}$
B)
$\sqrt{54} \div \sqrt{6}$
C)
$\sqrt[3]{32} \div \sqrt{8}$
D)
$\sqrt[4]{120} \div ( - \sqrt[3]{24})$
E(
$\sqrt{16} \div \sqrt{8}$
F)
$\sqrt[4]{64} \div \sqrt{2}$
​

Answer 1

Resposta:

A) $2$; B) $3$; C) $\sqrt[6]{2}$; D) $-\frac{\sqrt[4]{5} }{\sqrt[12]{24} }$; E) $\sqrt{2}$; F) $2$

Explicação passo a passo:

A)

$\frac{\sqrt[3]{40} }{\sqrt[3]{5} } =\frac{\sqrt[3]{5.(8)} }{\sqrt[3]{5} } =\frac{2.\sqrt[3]{5} }{\sqrt[3]{5} } =2.(1)=2$

B)

$\frac{\sqrt{54} }{\sqrt{6} } =\frac{\sqrt{6.(9)} }{\sqrt{6} } =3.\frac{\sqrt{6} }{\sqrt{6} } =3.(1)=3$

C)

$\frac{\sqrt[3]{32} }{\sqrt{8} } = \frac{\sqrt[3]{4.(8)} }{\sqrt{8} } =\frac{\sqrt[3]{4}.\sqrt[3]{8} }{\sqrt{8} } =\sqrt[3]{4} .\frac{8^{\frac{1}{3} } }{8^{\frac{1}{2} } } =\sqrt[3]{4} .(8^{-\frac{1}{6} } )=\frac{\sqrt[3]{4}}{\sqrt[6]{8} } =$

$\frac{\sqrt[3]{2.(2)}}{\sqrt[6]{2.(4)} } =\frac{\sqrt[3]{2}.\sqrt[3]{2} }{\sqrt[6]{2}\sqrt[6]{4} } =\frac{\sqrt[3]{2} }{\sqrt[6]{4} } .\frac{2^{\frac{1}{3} } }{2^{\frac{1}{6} } }=\frac{\sqrt[3]{2} }{\sqrt[6]{4} }.2^{\frac{1}{6} } =\frac{\sqrt[3]{2} }{\sqrt[6]{4} }.\sqrt[6]{2} }=$

$\frac{\sqrt[3]{2} }{\sqrt[6]{2.(2)} }.\sqrt[6]{2} }=\frac{\sqrt[3]{2} }{\sqrt[6]{2} }.\frac{\sqrt[6]{2}}{\sqrt[6]{2}} }=\frac{\sqrt[3]{2} }{\sqrt[6]{2} }.1=\frac{2^{\frac{1}{3} } }{2^{\frac{1}{6} } }=2^{\frac{1}{6} } =\sqrt[6]{2}$

D)

$\frac{\sqrt[4]{120} }{-(\sqrt[3]{24}) } =-\frac{\sqrt[4]{5.(24)} }{\sqrt[3]{24})}=-\frac{\sqrt[4]{5}.\sqrt[4]{24} }{\sqrt[3]{24} } =-\sqrt[4]{5} .\frac{24^{\frac{1}{4} } }{24^{\frac{1}{3} } } =-\frac{\sqrt[4]{5} }{\sqrt[12]{24} }$

E)

$\frac{\sqrt{16} }{\sqrt{8} } =\frac{\sqrt{2.(8)} }{\sqrt{8} } =\sqrt{2} .\frac{\sqrt{8} }{\sqrt{8} }=\sqrt{2}$

F)

$\frac{\sqrt[4]{64} }{\sqrt{2} } =\frac{\sqrt[4]{8.(8)} }{\sqrt{2} } =\frac{\sqrt[4]{8} .\sqrt[4]{8} }{\sqrt{2} } =\sqrt[4]{8} .\frac{\sqrt[4]{2.(4)} }{\sqrt{2} } =$

$\sqrt[4]{8} .\sqrt[4]{4}. \frac{\sqrt[4]{2} }{\sqrt{2} } =\sqrt[4]{8} .\sqrt[4]{4}. \frac{2^{\frac{1}{4} } }{2^{\frac{1}{2} } } =\sqrt[4]{8} .\sqrt[4]{4}. (2^{-\frac{1}{4} }) =$

$\frac{\sqrt[4]{8} .\sqrt[4]{4} }{\sqrt[4]{2} } =\frac{\sqrt[4]{2} .\sqrt[4]{4} .\sqrt[4]{4} }{\sqrt[4]{2} } =(\sqrt[4]{4} )^{2} =\sqrt{4} =2$