Question

efetue:
$( \sqrt{8} + \sqrt[3]{12} + \sqrt[4]{4} ) \div \sqrt{2}$
a resposta é
$3 + \sqrt[6]{18}$
não consigo chegar a esse resultado. ajuda Por favor ​

Answer 1

Resposta:

$( \sqrt{8} + \sqrt[3]{12} + \sqrt[4]{4} ) \div \sqrt{2} \\ \\ ( \sqrt{ {2}^{3} } + \sqrt[3]{3 \times 4} + \sqrt[4]{ {2}^{2} } ) \div {2}^{ \frac{1}{2} } \\ \\ ( {2}^{ \frac{3}{2} } + {12}^{ \frac{1}{3} } + {2}^{ \frac{1}{2} } ) \div {2}^{ \frac{1}{2} } \\ \\ \frac{ {2}^{ \frac{3}{2} } }{ {2}^{ \frac{1}{2} } } + \frac{(3 \times 4) {}^{ \frac{1}{3} } }{ {2}^{ \frac{1}{2} } } + \frac{ {2}^{ \frac{1}{2} } }{ {2}^{ \frac{1}{2} } } \\ \\ {2}^{ \frac{3}{2} - \frac{1}{2} } + \frac{ {3}^{ \frac{1}{3}} \times {2}^{ \frac{2}{3} } } { {2}^{ \frac{1}{2} } } + 1 \\ \\ {2}^{1} + {3}^{ \frac{1}{3} } \times {2}^{ \frac{2}{3} - \frac{1}{2} } + 1 \\ \\ 3 + {3}^{ \frac{1}{3}} \times {2}^{ \frac{4 - 3}{6} } \\ \\ 3 + {3}^{ \frac{1}{3} } \times {2}^{ \frac{1}{6} } \\ \\ 3 + \sqrt[3]{3} \times \sqrt[6]{2} \\ \\ MMC \: de \: 3\: e \: 6 = 6 \\ \\ 3 + \sqrt[3 \times 2]{ {3}^{2} } \times \sqrt[6]{ {2}^{1} } \\ \\ 3 + \sqrt[6]{9} \times \sqrt[6]{2} \\ \\ 3 + \sqrt[6]{9 \times 2} \\ \\ 3 + \sqrt[6]{18}$

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