Value Comparison Exercise: Finding the Largest Among Given Numbers

To solve this problem, we need to express each nested root as a power of 2:

• For $\sqrt{\sqrt{2}}$:
  $\sqrt{\sqrt{2}} = 2^{1/4}$
• For $\sqrt[3]{\sqrt{2}}$:
  $\sqrt[3]{\sqrt{2}} = 2^{1/6}$
• For $\sqrt[4]{\sqrt{2}}$:
  $\sqrt[4]{\sqrt{2}} = 2^{1/8}$
• For $\sqrt[5]{\sqrt{2}}$:
  $\sqrt[5]{\sqrt{2}} = 2^{1/10}$

Now, we compare these powers:

• $2^{1/4} > 2^{1/6} > 2^{1/8} > 2^{1/10}$.

Therefore, the largest value is $\sqrt{\sqrt{2}}$, which corresponds to choice 1.