Solve Nested Square Roots: √√49 × √√16 Multiplication Problem

To find the value of $\sqrt{\sqrt{49}} \cdot \sqrt{\sqrt{16}}$, we will follow these steps:

• Step 1: Simplify $\sqrt{\sqrt{49}}$.
• Step 2: Simplify $\sqrt{\sqrt{16}}$.
• Step 3: Multiply the simplified results together.

Step 1: $\sqrt{\sqrt{49}}$
- Calculate $\sqrt{49} = 7$.
- Therefore, $\sqrt{\sqrt{49}} = \sqrt{7}$.

Step 2: $\sqrt{\sqrt{16}}$
- Calculate $\sqrt{16} = 4$.
- Therefore, $\sqrt{\sqrt{16}} = \sqrt{4} = 2$.

Step 3: Multiply the simplified results:
- Multiply $\sqrt{7}$ by $2$.
- The product is $2 \cdot \sqrt{7} = 2\sqrt{7}$.

Therefore, the value of $\sqrt{\sqrt{49}} \cdot \sqrt{\sqrt{16}}$ is $\mathbf{2\sqrt{7}}$.