Solve √(36/144) × √√16: Multiple Square Root Operations

To solve the expression $\sqrt{\frac{36}{144}} \cdot \sqrt{\sqrt{16}}$, follow these steps:

• Simplify $\sqrt{\frac{36}{144}}$:
  - Evaluate the fraction: $\frac{36}{144} = \frac{1}{4}$.
  - Take the square root: $\sqrt{\frac{1}{4}} = \frac{1}{2}$ because $\sqrt{1} = 1$ and $\sqrt{4} = 2$.
• Simplify $\sqrt{\sqrt{16}}$:
  - First evaluate the inner square root: $\sqrt{16} = 4$ since $4^2 = 16$.
  - Then take the square root of the result: $\sqrt{4} = 2$ since $2^2 = 4$.
• Multiply the results from both parts:
  - Multiply the simplified results: $\frac{1}{2} \cdot 2 = 1$.

Therefore, the solution to the expression is $1$.