Question

simplifique os radicais ³√108​

Answer 1

$\sf \large{\sqrt[\sf 3]{\sf 108}}\\\\\\\sf \lage{=\sqrt[\sf 3]{\sf 2^2\cdot \:3^3}}\\\\\\\sf \large{\sqrt[\sf n]{\sf ab}=\sqrt[\sf n]{\sf a}\sqrt[\sf n]{\sf b}},\:\quad \:a\ge 0,\:b\ge 0\\\\\\\sf \large{\sqrt[\sf 3]{\sf 2^2\cdot \:3^3}=\sqrt[\sf 3]{\sf 2^2}\sqrt[\sf 3]{\sf 3^3}}\\\\\\\\\sf \large{=\sqrt[\sf 3]{\sf 2^2}\sqrt[\sf 3]{\sf 3^3}}\\\\\\\sf \large{=\sqrt[\sf 3]{\sf 2^2}\cdot \:3}\\\\\\\sf \large{=\sqrt[\sf 3]{\sf 4}\cdot \:3}$

$\boxed{S= \large{S=3\sqrt[\sf 3]{\sf 4} \approx 4.762203156}$