Question

Utilize as propriedades dos radicais para determinar o valor de cada expressão a seguir.

Answer 1

$a)\ ( \sqrt[5]{ \sqrt[3]{125} })= \sqrt[5]{5}=\ \textgreater \ \boxed{5^{\frac{1}{5}}}\\\\\\b) \sqrt{32} \cdot \sqrt{2}= \sqrt{32\cdot2}= \sqrt{64} =\ \textgreater \ \boxed{8}$

$c)\ ( \sqrt{0,0025}\cdot \sqrt[6]{0,000064})^2=\\\\ (\sqrt{ \frac{25}{10\ 000} }\cdot \sqrt[6]{ \frac{64}{1\ 000\ 000} })^2 =\\\\ ( \sqrt{ \frac{25}{10\ 000} }\cdot \sqrt[6]{ \frac{4^3}{100^3} })^2=\\\\ ( \sqrt{ \frac{25}{10\ 000} } \cdot \sqrt[6:3]{ \frac{4}{100} })^2=\\\\ (\sqrt{ \frac{25}{10\ 000} }\cdot \sqrt{ \frac{4}{100} } )^2= \\\\ ( \sqrt{ \frac{25\cdot4}{10\ 000\cdot100} })^2=\\\\ ( \sqrt{ \frac{100}{1\ 000\ 000} } )^2=\\\\ \frac{100^{\div100}}{1\ 000\ 000^{\div100}}=$
$=\ \textgreater \ \boxed{\frac{1}{10\ 000}}$

$d)\ ( \sqrt[5]{ \sqrt{1024} }\cdot \frac{ \sqrt[3]{125} }{ \sqrt[3]{25} })^{-1}=\\\\ ( \sqrt[5]{32} \cdot \frac{5}{ \sqrt[3]{25} } )^{-1}=\\\\ (2\cdot \frac{5}{ \sqrt[3]{25} } )^{-1}=\\\\ ( \frac{2\cdot5}{ \sqrt[3]{25} })^{-1}=( \frac{10}{ \sqrt[3]{25} } )^{-1}=\\\\ ( \frac{ \sqrt[3]{25} }{10})^1=\ \textgreater \ \boxed{ \frac{ \sqrt[3]{25} }{10}}$