Question

$if \: \sqrt[2]{x \div 0.0064} = \sqrt[3]{0.008}$
then the value of x

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Answer 1

$\tt{}\sqrt[2]{x \div 0.0064} = \sqrt[3]{0.008} \\ \\ \tt {\bigg( \frac{x}{0.0064} \bigg) }^{ \frac{1}{2} } = {\bigg( 0.008 \bigg) }^{ \frac{1}{3} } \\ \\ \tt \frac{ \sqrt[2]{x} }{ \sqrt[2]{0.0064} } = \sqrt[3]{0.008} \\ \\ \tt \sqrt[2]{x} = \sqrt[3]{0.008} \times \sqrt[2]{0.0064} \\ \\ \tt{ \sqrt[2]{x} } = {\bigg( \frac{8}{1000} \bigg)}^{ \frac{1}{3} } \times {\bigg( \frac{64}{10000} \bigg)}^{ \frac{1}{2} } \\ \\ \tt \sqrt[2]{x} = \frac{ \sqrt[3]{8} }{ \sqrt[3]{1000} } \times \frac{ \sqrt[2]{64} }{ \sqrt[2]{10000} } \\ \\ \tt \sqrt[2]{x} = \frac{2}{10} \times \frac{8}{100} \\ \\ \tt {( \sqrt[2]{x} )}^{2} = {( 0.2 \times 0.08 )}^{2} \\ \tt{}x = {(0.016)}^{2} \\ \boxed{ \huge \sf x = \red{ 0.000256}}$