Question

efetue e simplifique o resultado?
$\sqrt{2 \times \sqrt{27 = } }$
$\sqrt{90 \div \sqrt{5} }$
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Answer 1

  $\sqrt{2\times \sqrt{27}}=$

$=\sqrt{2\times \sqrt{3^{3}}}=$

$=\sqrt{2\times \sqrt{3\times 3^{2}}}=$

$=\sqrt{2\times 3\sqrt{3}}=$

$=\sqrt{6\sqrt{3}}=$

$=\sqrt{6}\sqrt{\sqrt{3}}}=$

$=\sqrt{6}\sqrt[4]{3}}$

  $\sqrt{90\div \sqrt{5}}=$

$=\sqrt{\frac{90}{\sqrt{5}}}=$

$=\sqrt{\frac{2\times 3^{2}\times 5}{5^{\frac{1}{2}}}}=$

$=\sqrt{2\times 3^{2}\times\frac{ 5}{5^{\frac{1}{2}}}}=$

$=\sqrt{2\times 3^{2}\times 5^{1-\frac{1}{2}}}=$

$=\sqrt{2\times 3^{2}\times 5^{\frac{1}{2}}}=$

$=\sqrt{2\times 3^{2}\times \sqrt{5}}=$

$=\sqrt{2}\times \sqrt{3^{2}}\times \sqrt{\sqrt{5}}}=$

$=\sqrt{2}\times 3\times \sqrt[4]{5}=$

$=3\sqrt{2}\sqrt[4]{5}$