Question

4) Na adição de raizes qual o valor da expressão abaixo?
2√3 +√27:
A) ( )3√7
B) 5√7
C) ( )3 √3
D) ( )5√3​

Answer 1

Oie, tudo bom?

Resposta: D) 5√3.

$= 2 \sqrt{3} + \sqrt{27}$

$= 2 \sqrt{3} + \sqrt{3 {}^{3} }$

$= 2 \sqrt{3} + \sqrt{3 {}^{2 + 1} }$

$= 2 \sqrt{3} + \sqrt{3 {}^{2} \: . \: 3 {}^{1} }$

$= 2 \sqrt{3} + \sqrt{3 {}^{2} \: . \: 3}$

$= 2 \sqrt{3} + \sqrt{3 {}^{2} } \sqrt{3}$

$= 2 \sqrt{3} + 3 \sqrt{3}$

$= (2 + 3) \sqrt{3}$

$\boxed{ = 5 \sqrt{3} }$

Att. NLE Top Shotta

Answer 2

$\Large\boxed{\begin{array}{l}\begin{array}{c|l}\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 27=3^2\cdot3\\\sf\sqrt{27}=\sqrt{3^{\backslash\!\!\!2}\cdot3}=3\sqrt{3}\\\sf 2\sqrt{3}+\sqrt{27}=2\sqrt{3}+3\sqrt{3}\\\sf2\sqrt{3}+\sqrt{27}=5\sqrt{3}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~D}}}}\end{array}}$