Question

O radical equivalente a ∛3. √4 é: a. Raiz sexta de 200 b. Raiz sexta de 576 c. Raiz sexta de 60 d. Raiz sexta de 70

Answer 1

Explicação passo-a-passo:

$\sf \sqrt[3]{3}\cdot\sqrt{4}$

$\sf =\sqrt[3]{3}\cdot\sqrt[2]{2^2}$

$\sf =\sqrt[6]{3^2}\cdot\sqrt[6]{2^6}$

$\sf =\sqrt[6]{3^2\cdot2^6}$

$\sf =\sqrt[6]{9\cdot64}$

$\sf =\sqrt[6]{576}$

Letra B

Answer 2

$\boxed{\begin{array}{c}\sf{Para~multiplicar~dois~radicais~de}\\\sf{\acute{i}ndices~diferentes~\acute{e}~necess\acute{a}rio} \\\sf{reduz\acute{i}-los~ao~mesmo~\acute{i}ndice}\end{array}}$

$\begin{array}{c|l}3,2&2\\3,1&3\\1\end{array}$

$\sf{mmc(3,2)=6}\\\sf{\sqrt[3]{3}\cdot\sqrt{4}=\sqrt[6]{3^2}\cdot\sqrt[6]{4^3}}\\\sf{\sqrt[6]{9\cdot64} =\sqrt[6]{576}}$