Question

fatore o numero que aparece no radicando e a seguir simplifique cada um dos radicais retirando fatores do radicando.
$\sqrt{75}$
$\sqrt{700}$
$\sqrt[3]{250}$
$\sqrt[5]{192}$
$\sqrt[4]{176}$
$\sqrt{800}$
$1800$
$\sqrt[3]{375}$
$\sqrt{2700}$
$\sqrt[6]{640}$
​

Answer 1

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 75=3\cdot5^2\\\sf\sqrt{75}=\sqrt{3\cdot5^2}=5\sqrt{3}\checkmark\\\begin{array}{c|c}\sf700&\sf2\\\sf350&\sf2\\\sf175&\sf5\\\sf35&\sf5\\\sf7&\sf7\\\sf1\end{array}\\\sf 700=2^2\cdot5^2\cdot7\\\sf\sqrt{700}=\sqrt{2^2\cdot5^2\cdot7}=10\sqrt{7}\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf250&\sf2\\\sf125&\sf5\\\sf25&\sf5\\\s5&\sf5\\\sf1\end{array}\\\sf 250=2\cdot5^3\\\sf\sqrt[\sf3]{\sf250}=\sqrt[\sf3]{\sf2\cdot5^3}=5\sqrt[\sf3]{\sf2}\\\begin{array}{c|c}\sf192&\sf2\\\sf96&\sf2\\\sf48&\sf2\\\sf24&\sf2\\\sf12&\sf2\\\sf6&\sf2\\\sf3&\sf3\\\sf1\end{array}\\\sf\sqrt[\sf5]{\sf192}=\sqrt[\sf5]{\sf2^5\cdot2\cdot3}=2\sqrt[\sf5]{\sf6}\checkmark\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf176&\sf2\\\sf88&\sf2\\\sf44&\sf2\\\sf22&\sf2\\\sf11&\sf11\\\sf1\end{array}\\\sf\sqrt[\sf4]{\sf176}=\sqrt[\sf4]{\sf2^4\cdot11}=2\sqrt[\sf4]{\sf11}\\\begin{array}{c|c}\sf800&\sf2\\\sf400&\sf2\\\sf200&\sf2\\\sf100&\sf2\\\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf\sqrt{800}=\sqrt{2^2\cdot2^2\cdot2\cdot5^2}=20\sqrt{2}\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf1800&\sf2\\\sf900&\sf2\\\sf450&\sf2\\\sf225&\sf3\\\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 1800=2^2\cdot2\cdot3^2\cdot5^2\\\sf\sqrt{1800}=\sqrt{2^2\cdot2\cdot3^2\cdot5^2}\\\sf\sqrt{1800}=30\sqrt{2}\\\begin{array}{c|c}\sf375&\sf3\\\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 375=3\cdot5^3\\\sf\sqrt[\sf3]{\sf375}=\sqrt[\sf3]{\sf3\cdot5^3}=5\sqrt[\sf3]{\sf3}\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf2700&\sf2\\\sf1350&\sf2\\\sf675&\sf3\\\sf225&\sf3\\\sf75&\sf3\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf2700=2^2\cdot3^2\cdot3\cdot5^2\\\sf\sqrt{2700}=\sqrt{2^2\cdot3^2\cdot3\cdot5^2}\\\sf\sqrt{2700}=30\sqrt{3}\\\begin{array}{c|c}\sf640&\sf2\\\sf320&\sf2\\\sf160&\sf2\\\sf80&\sf2\\\sf40&\sf2\\\sf20&\sf2\\\sf10&\sf2\\\sf5&\sf5\\\sf1\end{array}\\\sf 640=2^6\cdot2\cdot5\\\sf\sqrt[\sf6]{\sf640}=\sqrt[\sf6]{\sf2^6\cdot2\cdot5}=2\sqrt[\sf6]{\sf10}\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\boldsymbol{Selecione\,a\,melhor\,resposta}}\\\underline{\boldsymbol{assim\,que\,a\,opc_{\!\!,}\tilde ao\,estiver\,dispon\acute ivel}}\\\underline{\boldsymbol{para\,motivar\,os\,respondedores.}}\end{array}}$