Question

decomponha o radicando em fatores primos e determine o valor das raízes exatas abaixo:​

Answer 1

$\Large\boxed{\begin{array}{l}\rm a)\\\begin{array}{c|c}\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\\\sf 16=2^4\\\sf \sqrt[\sf4]{\sf 16}=\sqrt[\sf4]{\sf 2^4}=2\checkmark\end{array}}$

$\Large\boxed{\begin{array}{l}\rm b)\\\begin{array}{c|c}\sf243&\sf3\\\sf81&\sf3\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 243=3^5\\\sf\sqrt[\sf5]{\sf243}=\sqrt[\sf5]{\sf3^5}=3\end{array}}$

$\Large\boxed{\begin{array}{l}\rm c)\\\begin{array}{c|c}\sf625&\sf5\\\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 625=5^4\\\sf\sqrt[\sf4]{\sf625}=\sqrt[\sf4]{\sf 5^4}=5\end{array}}$

$\Large\boxed{\begin{array}{l}\rm d)\\\begin{array}{c|c}\sf81&\sf3\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf\sqrt[\sf4]{\sf81}=\sqrt[\sf4]{\sf3^4}=3\end{array}}$