Question

2 - Decomponha o radicando em fatores primos e , em seguida, simplifique cada um dos radicais.
a)
$\sqrt[10]{32}$
b)
$\sqrt[9]{27}$
c)
$\sqrt[16]{81}$
d)
$\sqrt[6]{16}$
e)
$\sqrt[8]{64}$
f)
$\sqrt[12]{1024}$
​

Answer 1

$$\begin{lgathered}a)~~ \sqrt[10]{32} = \sqrt[10:5]{2^{5:5}} = \sqrt{2} \\ \\ b) \sqrt[~9]{27} = \sqrt[9:3]{3^{3:3}} = \sqrt[3]{3} \\ \\ c)~~ \sqrt[16]{81} = \sqrt[16:4]{3^{4:4}} = \sqrt[4]{3} \\ \\ d)~~ \sqrt[6]{16} = \sqrt[6:2]{2^{4:2}} = \sqrt[3]{2^2} \\ \\ e)~~ \sqrt[8]{64} = \sqrt[8:2]{2^{6:2}} = \sqrt[4]{2^3} \\ \\ f)~~ \sqrt[12]{1024} = \sqrt[12:2]{2^{10:2}} = \sqrt[6]{2^5}\end{lgathered}$$