Solve the Nested Radical: Finding √√2

To solve $\sqrt{\sqrt{2}}$, we will use the property of roots.

• Step 1: Recognize that $\sqrt{\sqrt{2}}$ involves two square roots.
• Step 2: Each square root can be expressed using exponents: $\sqrt{2} = 2^{1/2}$.
• Step 3: Therefore, $\sqrt{\sqrt{2}} = (2^{1/2})^{1/2}$.
• Step 4: Apply the formula for the root of a root: $(x^{a})^{b} = x^{ab}$.
• Step 5: For $(2^{1/2})^{1/2}$, this means we compute the product of the exponents: $(1/2) \times (1/2) = 1/4$.
• Step 6: The expression simplifies to $2^{1/4}$, which is written as $\sqrt[4]{2}$.

Therefore, $\sqrt{\sqrt{2}} = \sqrt[4]{2}$.

This corresponds to choice 2: $\sqrt[4]{2}$.

The solution to the problem is $\sqrt[4]{2}$.