Question

por favor me ajudem a que quero saber e a que esta circulada

Answer 1

$\sqrt[3]{ \sqrt{32} }. \sqrt{ \sqrt[3]{2} }=$

$\sqrt[6]{32}. \sqrt[6]{2}= \sqrt[6]{64}= \sqrt[6]{2^6}=2$

Answer 2

Observe que, $\sqrt[a]{\sqrt[b]{c}}=\sqrt[a\cdot b]{c}$.

Como $32=2^5$, então $\sqrt[3]{\sqrt{32}}=\sqrt[6]{2^5}$

Analogamente, $\sqrt[2]{\sqrt[3]{2}}=\sqrt[6]{2}$.

Portanto, $\sqrt[3]{\sqrt{32}}\cdot\sqrt[2]{\sqrt[3]{2}}=\sqrt[6]{2^5}\cdot\sqrt[6]{2}$

Temos que, $\sqrt[6]{2^5}\cdot\sqrt[6]{2}=\sqrt[6]{2^6}=2$.

Logo, $\sqrt[3]{\sqrt{32}}\cdot\sqrt[2]{\sqrt[3]{2}}=2$