1. The problem is to simplify $\sqrt{\sqrt{625}}$. 2. Recall that $\sqrt{a}$ means the square root of $a$, and $\sqrt{\sqrt{a}}$ means the square root of the square root of $a$. 3. First, find the inner square root: $\sqrt{625}$. 4. Since $625 = 25^2$, $\sqrt{625} = 25$. 5. Now, find the square root of the result: $\sqrt{25}$. 6. Since $25 = 5^2$, $\sqrt{25} = 5$. 7. Therefore, $\sqrt{\sqrt{625}} = 5$.