Solve Nested Square Roots: Simplifying √(√625) Step by Step

To solve this problem, we'll follow these steps:

• Step 1: Evaluate the innermost square root, $\sqrt{625}$.
• Step 2: Evaluate the square root of the result from Step 1.

Now, let's work through each step:

Step 1: Evaluate $\sqrt{625}$.
The square root of 625 is 25, since $25 \times 25 = 625$. Thus, $\sqrt{625} = 25$.

Step 2: Evaluate $\sqrt{25}$.
The square root of 25 is 5, since $5 \times 5 = 25$. Thus, $\sqrt{25} = 5$.

Therefore, the solution to the problem $\sqrt{\sqrt{625}}$ is 5.