Question

Multiplique os radicais e simplifique os produtos obtidos:(quando possível)

a)
$\sqrt{5 \times \sqrt{20} } =$
b)
$\sqrt[4]{8} \times \sqrt[4]{32} =$
c)
$\sqrt[5]{4} \times \sqrt[5]{9} =$
d)
$\sqrt[3]{6} \times \sqrt[3]{9} =$
e)
$\sqrt{6 \times \sqrt{12} } =$
f)
$\sqrt[3]{12} \times \sqrt[3]{6} =$

​

Answer 1

Resposta:

$a) \sqrt{5 \times \sqrt{20} } = \sqrt[4]{25 \times 20} = \sqrt[4]{500} \\ </p><p>b) \sqrt[4]{8} \times \sqrt[4]{32} = \sqrt[4]{ {2}^{3} \times {2}^{5} } = {2}^{2} = 4 \\ </p><p>c) \sqrt[5]{4} \times \sqrt[5]{9} = \sqrt[5]{4 \times 9} = \sqrt[5]{36} \\ </p><p>d) \sqrt[3]{6} \times \sqrt[3]{9} = 3 \sqrt{2}$

$e) \sqrt{6 \times \sqrt{12} } = \sqrt[4]{36 \times 12} = \sqrt[4]{ {2}^{2} \times {3}^{2} \times {2}^{2} \times 3 } = 4 \times 3 = 12 \\ </p><p>f) \sqrt[3]{12} \times \sqrt[3]{6} = \sqrt[3]{ {2}^{2} \times 2 \times 3 } = 2 \sqrt[3]{3}$