Question

$\sqrt{200. \sqrt{10} }$
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Answer 1

$\sqrt{200\sqrt{10} } =\sqrt[4]{200^2.10}$

$\sqrt[4]{200^2.10} = \sqrt[4]{400000}$

Fatorando 400.000:

400.000 / 2

200.000 / 2

100.000 / 2

50.000 / 2

25.000 / 5

5.000 / 2

2500 / 2

1250 / 2

625 / 5

125 / 5

25 / 5

5 / 5

1

Totalizando: 2^7 . 5^5

$\sqrt[4]{400000} = \sqrt[4]{2^4 . 2^3 . 5^4.5}$

$\sqrt[4]{2^4 . 2^3 . 5^4.5}=2.5\sqrt[4]{2^3.5}$

$2.5\sqrt[4]{2^3.5} = 10\sqrt[4]{40}$