Question

simplifique as expressões

a) √50-√8

b) √80 + √180​

Answer 1

Resposta:

a)

$\sqrt[4]{4} \times ( \sqrt{5} - \sqrt{2} ) \times ( \sqrt{5} + \sqrt{2})$

b)

$\sqrt[6]{20} \sqrt[3]{5} \times ( \sqrt[3]{2} + \sqrt[3]{3} \times (2 \sqrt[3]{2} - 2 \sqrt[3]{3} + \sqrt[3]{36} )$

.

Explicação passo-a-passo:

a) $\sqrt{50} - \sqrt{8} \\ ( \sqrt[4]{50} - \sqrt[4]{8} ) \times ( \sqrt[4]{50} + \sqrt[4]{8}) \\ \sqrt[4]{2} \times ( \sqrt[4]{25} - \sqrt[4]{4} ) \sqrt[4]{2} \times (\sqrt[4]{25} + \sqrt[4]{4}) \\ \sqrt[4]{2} \times( \sqrt[4]{ {5}^{2} } - \sqrt[4]{ {2}^{2} } ) \sqrt[4]{2} \times ( \sqrt[4]{ {5}^{2} } - \sqrt[4]{ {2}^{2} } ) \\ \sqrt[4]{2} \times ( \sqrt{5} - \sqrt{2} ) \sqrt[4]{2} \times ( \sqrt{5} + \sqrt{2}) \\ \sqrt[4]{2} \sqrt[4]{2} \times ( \sqrt{5} - \sqrt{2} ) \times ( \sqrt{5} + \sqrt{2} ) \\ \sqrt[4]{4} \times ( \sqrt{5} - \sqrt{2} ) \times ( \sqrt{5} + \sqrt{2} )$

$\sqrt{80} + \sqrt{180} \\ ( \sqrt[6]{80} + \sqrt[6]{180} ) \times ( \sqrt[3]{80} - \sqrt[6]{14400} + \sqrt[3]{80} ) \\ \sqrt[6]{20} \times ( \sqrt[6]{4} + \sqrt[6]{9 } ) \times (2 \sqrt[3]{10} - 2 \sqrt[6]{225} + \sqrt[3]{180} ) \\ \sqrt[6]{20} \times ( \sqrt[6]{ {2}^{2} } + \sqrt[6]{ {3}^{2} }) \times (2 \sqrt[3]{10} - 2 \sqrt[6]{ {15}^{2} } + \sqrt[3]{180} ) \\ \sqrt[6]{20} \times ( \sqrt[3]{2} + \sqrt[3]{3} ) \times (2 \sqrt[3]{10} - 2 \sqrt[3]{15} + \sqrt[3]{180} \\ \sqrt[6]{20} \times ( \sqrt[3]{2} + \sqrt[3]{3} ) \sqrt[3]{5} \times (2 \sqrt[3]{2} - 2 \sqrt[3]{3} + \sqrt[3]{36} ) \\ \sqrt[6]{20} \sqrt[3]{5} \times ( \sqrt[3]{2} + \sqrt[3]{3} \times (2 \sqrt[3]{2} - 2 \sqrt[3]{3} + \sqrt[3]{36} )$