Question

∛375 e √800 Fatorando o numero do radicando e simplificando cada uma das raízes, encontramos, respectivamente:
ME AJUDEM POR FAVOR!!

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a)\:\sqrt[\mathsf{3}]{\mathsf{375}} = \sqrt[\mathsf{3}]{\mathsf{125.3}} = \sqrt[\mathsf{3}]{\mathsf{5^3.3}} = 5\sqrt[\mathsf{3}]{\mathsf{3}}}$

$\mathsf{b)\:\sqrt{\mathsf{800}} = \sqrt{\mathsf{2.16.25}} = \sqrt{\mathsf{2.4^2.5^2}} = 4.5\sqrt{\mathsf{2}} = 20\sqrt{\mathsf{2}}}$

Answer 2

$\Large\boxed{\begin{array}{l} \begin{array}{r|l}\sf375&\sf3\\\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf\sqrt[\sf3]{375}=\sqrt[\sf3]{3\cdot5^3}\\\sf\sqrt[\sf3]{375}=5\sqrt[\sf3]{3}\end{array}}$

$\Large\boxed{\begin{array}{l} \begin{array}{r|l}\sf800&\sf2\\\sf400&\sf2\\\sf200&\sf2\\\sf100&\sf2\\\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf\sqrt{800}=\sqrt{2^2\cdot2^2\cdot2\cdot5^2}\\\sf\sqrt{800}=2\cdot2\cdot5\sqrt{2}\\\sf\sqrt{800}=20\sqrt{2}\end{array}}$