Question

Calcule o resultado da expressão e assinale a alternativa correta:

(A) 200
(B) 165
(C) 145
(D) 110
(E) 100

Answer 1

Resposta:

Dica: resolva as raízes da direita pra esquerda.

$\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=\Big(\sqrt{98+2}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+4}}}\bigg)$]$\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=\Big(\sqrt{100}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{9}}}\bigg)$

$\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=(10)\cdot\Big(\sqrt{119+\sqrt{1+3}}\Big)$

$\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=(10)\cdot\Big(\sqrt{119+\sqrt{4}}\Big)$

$\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=(10)\cdot\big(\sqrt{119+2}\big)$

$\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=(10)\cdot\big(\sqrt{121}\big)$

$\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=(10)\cdot(11)$

$\red{\sf\Big(\sqrt{98+\sqrt{4}}\Big)\cdot\bigg(\sqrt{119+\sqrt{1+\sqrt{5+\sqrt{16}}}}\bigg)=110}$

Letra D