Question

Qual valor da expressão?

Answer 1

Explicação passo-a-passo:

${( \sqrt{ {( \frac{1}{6} )}^{3} \times (0.666...) } + \sqrt{ {( \frac{2}{3} )}^{0} - \frac{1}{(1.333...)} }) }^{ - \frac{1}{2} } = \\ \\ {( \sqrt{ \frac{1}{216} \times \frac{6}{9} } + \sqrt{1 - \frac{1}{ \frac{12}{9} } } ) }^{ - \frac{1}{2} } = \\ \\ {( \sqrt{ \frac{1}{216} \times \frac{2}{3} } + \sqrt{1 - \frac{1}{ \frac{4}{3} } } ) }^{ - \frac{1}{2} } \\ \\ {( \sqrt{ \frac{2}{648} } + \sqrt{1 - \frac{3}{4} }) }^{ - \frac{1}{2} } = \\ \\ {( \sqrt{ \frac{1}{324} } + \sqrt{ \frac{1}{4} } )}^{ - \frac{1}{2} } = \\ \\ {( \frac{1}{18} + \frac{1}{2} )}^{ - \frac{1}{2} } = \\ \\ {( \frac{1 + 9}{18} )}^{ - \frac{1}{2} } = \\ \\ {( \frac{10}{18} )}^{ - \frac{1}{2} } = \\ \\ {( \frac{5}{9} )}^{ - \frac{1}{2} } = \\ \\ \sqrt{ \frac{9}{5} } = \\ \\ \frac{ \sqrt{9} }{ \sqrt{5} } = \\ \\ \frac{3}{ \sqrt{5} } = \\ \\ \frac{3 \sqrt{5} }{5}$