Question

Simplificando 2√ 8 - 4√ 18 + √ 32=


a) √ 2 b) -√ 8 c) √ 8 d) -4√ 2 e) -2√ 2

Answer 1

Olá!
    
    Note que   $8=2^3,\;\;18=2\cdot 3^2\;\;\text{e}\;\;32=2^5.$   Daí, temos:


$2\sqrt{8}-4\sqrt{18}+\sqrt{32}=2\sqrt{2^3}-4\sqrt{2\cdot 3^2}+\sqrt{2^5}= \\ \\ = 2\sqrt{2^2\cdot 2}-4\sqrt{2}\cdot \sqrt{3^2}+\sqrt{2^2\cdot 2^2\cdot 2} = \\ \\ = 2\sqrt{2^2}\sqrt{2}-4\cdot 3\sqrt{2}+\sqrt{2^2}\sqrt{2^2}\sqrt{2} =\\ \\ = 2\cdot 2\sqrt{2}-12\sqrt{2}+2\cdot 2\sqrt{2} = 4\sqrt{2}-12\sqrt{2}+4\sqrt{2}=\\ \\ = \sqrt{2}(4-12+4)=-4\sqrt{2}.$


    Portanto,  resposta (D).


Bons estudos!