Question

decomponha o radicando em fatores primos e calcule o valor de cada radical​

Answer 1

Resposta:

$a)\ 2\\\\b)\ 7\\\\c)\ \frac{9}{4} \\\\d)\ 11\\\\e)\ \frac{5}{4} \\\\f)\ \frac{1}{4}$

Explicação passo a passo:

$a)\ \sqrt[5]{32} \\\\\sqrt[5]{2^{5} } \\\\2^{\frac{5}{5} } \\\\2^{1} \\\\2$

$b)\ \sqrt[3]{343} \\\\\sqrt[3]{7^{3} } \\\\7^{\frac{3}{3} } \\\\7^{1} \\\\7$

$c)\ \sqrt[3]{\frac{729}{64} } \\\\\sqrt[3]{\frac{3^{6} }{2^{6} } } \\\\\sqrt[3]{(\frac{3}{2})^{6} } \\\\(\frac{3}{2})^{\frac{6}{3} } \\\\(\frac{3}{2} )^{2} \\\\\frac{3^{2} }{2^{2} } \\\\\frac{9}{4}$

$d)\ \sqrt[2]{121} \\\\\sqrt[2]{11^{2} } \\\\11^{\frac{2}{2} } \\\\11^{1} \\\\11$

$e)\ \sqrt[4]{\frac{625}{256} } \\\\\sqrt[4]{\frac{5^{4} }{2^{8} } } \\\\\sqrt[4]{\frac{5^{4} }{2^{(2\times4)} } } \\\\\sqrt[4]{\frac{5^{4} }{(2^{2})^{4} } } \\\\\sqrt[4]{\frac{5^{4} }{4^{4} } } \\\\\sqrt[4]{(\frac{5}{4} )^{4} } \\\\(\frac{5}{4} )^{\frac{4}{4} } \\\\(\frac{5}{4} )^{1} \\\\\frac{5}{4}$

$f)\ \sqrt[5]{\frac{1}{1024} } \\\\\sqrt[5]{\frac{1^{5} }{2^{10} } } \\\\\sqrt[5]{\frac{1^{5} }{2^{(2\times5)} } }\\\\\sqrt[5]{\frac{1^{5} }{(2^{2})^{5} } }\\\\\sqrt[5]{\frac{1^{5} }{4^{5} } }\\\\\sqrt[5]{(\frac{1 }{4})^{5} }\\\\(\frac{1 }{4})^{\frac{5}{5} }\\\\(\frac{1 }{4})^{1 }\\\\\frac{1 }{4}$