Question

solve the following

$\sqrt[3]{ \sqrt{64} }$
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Answer 1

$\sqrt{64} = 8 \\ \\ \sqrt[3]{8} = 2 \\ \\ = 2$

Answer 2

$\sqrt[3]{\sqrt[]{64} }$  $= \left(64^{\frac{1}{2}}\right)^{\frac{1}{3}}$

$=64^{\frac{1}{2}\cdot \frac{1}{3}}$

$(\frac{1}{2}\cdot \frac{1}{3}=\frac{1}{6})$

$= 64^{\frac{1}{6}}$

$a^{\frac{1}{n}}=\sqrt[n]{a}$ $=\sqrt[6]{64}$

$\mathrm{Factor\:the\:number:\:}\:64=2^6$

$=\sqrt[6]{2^6}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt[6]{2^6}=2$

$so, our< answer> is. 2$