Question

Simplifique cada radical retirando fatores do radicando : a) ⁵√x¹¹=
b) ³√x⁵y⁷ =
c) √500 =
d) ⁶√320 =
me ajudemm ;( ​

Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf \sqrt[\sf5]{\sf x^{11}}=\sqrt[\sf5]{\sf (x^2)^5\cdot x}=x^2\sqrt[\sf5]{\sf x}\\\\\tt b)~\sf \sqrt[\sf3]{\sf x^5y^7}=\sqrt[\sf3]{\sf x^3\cdot x^2\cdot (y^2)^3\cdot y}\\\sf =xy^2\sqrt[\sf3]{\sf x^2y}\\\\\tt c)~\begin{array}{c|c}\sf500&\sf2\\\sf 250&\sf2\\\sf 125&\sf5\\\sf 25&\sf5\\\sf 5&\sf5\\\sf1\end{array}\\\sf 500=2^2\cdot 5^2\cdot5\\\sf\sqrt{500}=\sqrt{2^2\cdot5^2\cdot5}=2\cdot5\sqrt{5}=10\sqrt{5}\end{array}}$

$\large\boxed{\begin{array}{l}\tt d)~\begin{array}{c|c}\sf320&\sf2\\\sf160&\sf2\\\sf80&\sf2\\\sf40&\sf2\\\sf20&\sf2\\\sf10&\sf2\\\sf5&\sf5\\\sf1\end{array}\\\sf 320=2^6\cdot5\\\sf \sqrt[\sf6]{\sf320}=\sqrt[\sf6]{\sf2^6\cdot5}=2\sqrt[\sf6]{\sf5}\end{array}}$