Nested Root Simplification

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Q. \( \sqrt[4]{\sqrt[3]{\sqrt{2^2}}} \)

✏️ Solution

\( = \sqrt[4]{\sqrt[3]{2}} \)

\( = \sqrt[4]{2^{1/3}} \)

\( = 2^{\frac{1}{3} \times \frac{1}{4}} \)

\( = 2^{1/12} \)

\( \boxed{2^{1/12}} \)

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