The problem asks us to evaluate the nested square root: $\sqrt{\sqrt{144} \times \sqrt{169}}$.

1. Problem Description

The problem asks us to evaluate the nested square root: $\sqrt{\sqrt{144} \times \sqrt{169}}$.

2. Solution Steps

First, we need to find the square roots of 144 and

1

6

9. $\sqrt{144} = 12$

$\sqrt{169} = 13$

Next, we multiply the results:

$12 \times 13 = 156$

Finally, we take the square root of the result:

$\sqrt{156}$

To simplify $\sqrt{156}$, we can find the prime factorization of

1

5

6. $156 = 2 \times 78 = 2 \times 2 \times 39 = 2 \times 2 \times 3 \times 13 = 2^2 \times 3 \times 13$

So, $\sqrt{156} = \sqrt{2^2 \times 3 \times 13} = \sqrt{2^2} \times \sqrt{3 \times 13} = 2\sqrt{39}$.

3. Final Answer

The final answer is $2\sqrt{39}$.