Question

El 0.3 tiene un símbolo arriba
$( \sqrt{ \frac{1}{6} } \sqrt{ \frac{1}{6} } ) ^{ - 2} - ( \frac{ \sqrt{72} }{ \sqrt{2} } - \sqrt{ {0.3}^{4} } )$
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Answer 1

Respuesta:

Explicación paso a paso:

$i^{2}=-1\\\\\left(\sqrt{\frac{1}{6}}*\sqrt{-\frac{1}{6}}\right)^{-2}=\frac{1}{\left(\sqrt{\frac{1}{6}}*\sqrt{-\frac{1}{6}}\right)^{2}} \\\\\left(\sqrt{\frac{1}{6}}\sqrt{-\frac{1}{6}}\right)^{2}=\left(\sqrt{\frac{1}{6}}*\sqrt{-1}\sqrt{\frac{1}{6}}\right)^{2}=\\\\=\left(\sqrt{\frac{1}{6}}*\sqrt{\frac{1}{6}}i\right)^{2}=\left(\sqrt{\frac{1}{6}}\right)^{2}*\left(\sqrt{\frac{1}{6}}\right)^{2}*i^{2}=\\\\=\frac{1}{6}*\frac{1}{6}*(-1)=-\frac{1}{36}$

$\left(\sqrt{\frac{1}{6}}*\sqrt{\frac{-1}{6}}\right)^{-2}=$

$\frac{1}{\left(\sqrt{\frac{1}{6}}*\sqrt{-\frac{1}{6}}\right)^{2}}=\frac{1}{\frac{-1}{36}}=-36$

$\frac{\sqrt{72}}{\sqrt{2}}=\frac{\sqrt{(36)(2)}}{\sqrt{2}}=\\\\=\frac{\sqrt{36}\sqrt{2}}{\sqrt{2}}=\sqrt{36}=6\\\\(0.\hat{3})^{4}=\left(\frac{1}{3}\right)^{4}=\frac{1^{4}}{3^{4}}$

$\left(\sqrt{\frac{1}{6}}*\sqrt{-\frac{1}{6}}\right)^{-2}-\left(\frac{\sqrt{72}}{\sqrt{2}}-\sqrt{(0.\hat{3})^{4}}\right)=-36-\left(6-\sqrt{\frac{1^{4}}{3^{4}} }\right)=\\\\=-36-\left(6-\sqrt{\frac{1}{81}}\right)=-36-\left(6-\frac{1}{9}\right)=\\\\=-\frac{377}{9}$