Question

Simplifique os Radicais

² 180 =

² 240 =

³ 80 =

³ 112 =

⁴ 32 =

⁵ 128 =

Efetuar as simplificação dos radicais .

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Answer 1

Explicação passo-a-passo:

a) $\sqrt[2]{180}$

$\sf =\sqrt[2]{2^2\cdot3^2\cdot5}$

$\sf =2\cdot3\sqrt[2]{5}$

$\sf =6\sqrt[2]{5}$

b) $\sqrt[2]{240}$

$\sf =\sqrt[2]{2^4\cdot3\cdot5}$

$\sf =2^2\sqrt[2]{3\cdot5}$

$\sf =4\sqrt[2]{15}$

c) $\sqrt[3]{80}$

$\sf =\sqrt[3]{2^4\cdot5}$

$\sf =\sqrt[3]{2^3\cdot2\cdot5}$

$\sf =2\sqrt[3]{10}$

d) $\sqrt[3]{112}$

$\sf =\sqrt[3]{2^4\cdot7}$

$\sf =\sqrt[3]{2^3\cdot2\cdot7}$

$\sf =2\sqrt[3]{14}$

e) $\sqrt[4]{32}$

$\sf =\sqrt[4]{2^5}$

$\sf =\sqrt[4]{2^4\cdot2}$

$\sf =2\sqrt[4]{2}$

f) $\sqrt[5]{128}$

$\sf =\sqrt[5]{2^7}$

$\sf =\sqrt[5]{2^5\cdot2^2}$

$\sf =2\sqrt[5]{4}$