Question

simplifique a expressão $\sqrt 80 + \sqrt20$ e assinale a alternativa correta
a $6\sqrt5$
b $12\sqrt3$
c $2\sqrt5 + 5 \sqrt2$
d $6\sqrt14$
e $2 \sqrt5$

Answer 1

É só ir dividindo os números dentro das raízes por 2.

Answer 2

$\large\boxed{\begin{array}{l} \underline{\sf Primeiro\, vamos\, calcular\,as\, ra\acute{i}zes}\\\begin{array}{r|l}\sf80&\sf2\\\sf40&\sf2\\\sf20&\sf2\\\sf10&\sf2\\\sf5&\sf5\\\sf1\end{array}\quad\qquad\qquad~~\begin{array}{r|l}\sf20&\sf2\\\sf10&\sf2\\\sf5&\sf5\\\sf1\end{array}\\\sf\sqrt{80}=\sqrt{2^2\cdot2^2\cdot5}\quad\quad\sqrt{20}=\sqrt{2^2\cdot5}\\\sf\sqrt{80}=2\cdot2\sqrt{5}\quad\qquad~~\sqrt{20}=2\sqrt{5}\\\sf\sqrt{80}=4\sqrt{5}\end{array}}$

$\large\boxed{\begin{array}{l} \underline{\sf Agora\, vamos\, somar}\\\sf\sqrt{80}+\sqrt{20} = 4\sqrt{5}+2\sqrt{5}\\\sf \sqrt{80} + \sqrt{20 } = (4+2)\sqrt{5}\\\sf \sqrt{80} + \sqrt{20} = 6\sqrt{5}\\\huge\boxed{ \boxed{ \boxed{ \boxed{ \sf\dagger \maltese~ alternativa~A}}}}\end{array}}$