Question

05) Decomponha o radicando
er fatores primos e, em se-
guida, simplifique cada um dos
radicais
a)
$\sqrt[10]{32}$

b)
$\sqrt[9]{27}$
=
c)
$\sqrt[16]{81}$
=
d)
$\sqrt[6]{16}$
=
e)
$\sqrt[8]{64}$
=​

Answer 1

Resposta:

a) $32 = 2^5$

Assim: $\sqrt[10]{32} = \sqrt[10]{2^5} = \sqrt[10:5]{2^{5:5}} = \sqrt{2}$

b) $27 = 3^3$

$\sqrt[9]{27} = \sqrt[9]{3^3} = \sqrt[9:3]{3^{3:3}} = \sqrt[3]{3}$

c) $81 = 3^4$

$\sqrt[16]{81} = \sqrt[16]{3^4} = \sqrt[16:4]{3^{4:4}} = \sqrt[4]{3}$

d) $16 = 2^4$

$\sqrt[6]{16} = \sqrt[6]{2^4} = \sqrt[6:2]{2^{4:2}} = \sqrt[3]{2^2} = \sqrt[3]{4}$

e) $64 = 2^6$

$\sqrt[8]{64} = \sqrt[8]{2^6} = \sqrt[8:2]{2^{6:2}} = \sqrt[4]{2^3} = \sqrt[4]{8}$

Answer 2

Resposta:

Leia abaixo

Explicação passo-a-passo:

$\boxed{\sqrt[10]{32} = \sqrt[10]{2^5} = \sqrt{2}}$

$\boxed{\sqrt[9]{27} = \sqrt[9]{3^3} = \sqrt[3]{3} }$

$\boxed{\sqrt[16]{81} = \sqrt[16]{3^4} = \sqrt[4]{3} }$

$\boxed{\sqrt[6]{16} = \sqrt[6]{4^2} = \sqrt[3]{4} }$

$\boxed{\sqrt[8]{64} = \sqrt[8]{8^2} = \sqrt[4]{8} }$