Question

multiplique os ridicais e simplifique o produto obtido:

a) 5.\sqrt[3]{3}.\sqrt{7} =5\sqrt{21} ?

b) 18. \sqrt[3]{14} : 6. \sqrt[3]{7} ?

c) 10.\sqrt{8 } : 2\sqrt{2} ?

Answer 1

$a) 5.\sqrt[3]{3}.\sqrt{7} =5\sqrt{21}$
$5. \sqrt[3*2]{3^{1*2} } * \sqrt[2*3]{7^{1*3} } =5 \sqrt{21}$
$5. \sqrt[6]{ 3^{2} } * \sqrt[6]{7^{3} } =5\sqrt{21}$
$5. \sqrt[6]{3^{2} *7^{3} } =5\sqrt{21}$
$5. \sqrt[6]{9*343} =5\sqrt{21}$
$5. \sqrt[6]{3087} =5\sqrt{21}$
$\sqrt[6]{3087} = \sqrt{21}$ ===> $FALSO$

$b) 18. \sqrt[3]{14} : 6. \sqrt[3]{7} = \frac{18}{6} * \sqrt[3]{ \frac{14}{7} } =3 \sqrt[3]{2}$

$c) 10.\sqrt{8 } : 2\sqrt{2} = \frac{10}{2} * \sqrt{ \frac{8}{2} } =5 \sqrt{4} =5*2=10$