Question

Decomponha o radicando em fatores primos e, a seguir, resolva cada um dos radicais:

$\sqrt[10]{1024} =$
$\sqrt[3]{27} =$
$\sqrt[4]{81} =$
$\sqrt[6]{4096} =$


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Answer 1

explicaçao passo a passo

Answer 2

Explicação passo-a-passo:

a) $\sqrt[10]{1024}$

1024 | 2

512 | 2

256 | 2

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1

$1024=2^{10}$

$\sqrt[10]{1024}=\sqrt[10]{2^{10}}$

$\sqrt[10]{1024}=2$

b) $\sqrt[3]{27}$

27 | 3

9 | 3

3 | 3

1

$27=3^3$

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

$\sqrt[3]{27}=3$

c) $\sqrt[4]{81}$

81 | 3

27 | 3

9 | 3

3 | 3

1

$81=3^4$

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

$\sqrt[4]{81}=3$

d) $\sqrt[6]{4096}$

4096 | 2

2048 | 2

1024 | 2

512 | 2

256 | 2

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1

$4096=2^{12}$

$\sqrt[6]{4096}=\sqrt[6]{2^{12}}$

$\sqrt[6]{4096}=\sqrt[6]{(2^2)^6}$

$\sqrt[6]{4096}=2^2$

$\sqrt[6]{4096}=4$