Question

simplifique os radicais ​

Answer 1

Resposta:

Explicação passo-a-passo:

a) $\sqrt[3]{2^{7}.3^{5}.5^{4}}=\sqrt[3]{2^{6}.2.3^{3}.3^{2}.5^{3}.5}=2^{2}.3.5.\sqrt[3]{2.3^{2}.5}=60.\sqrt[3]{90}$

b) $\sqrt[3]{162}$, decompondo 162 em fatores primos:

162 | 2

81 | 3

27 | 3

9 | 3

3 | 3

1 |

Assim

$\sqrt[3]{162}$ = $\sqrt[3]{2.3^{3}.3}=3\sqrt[3]{6}$

c) $\sqrt[6]{3^{3}.4^{12}}=4^{2}\sqrt[6]{3^{3}}=16\sqrt[6]{27}$