The expression $\sqrt{248+\sqrt{52+\sqrt{144}}}$ is equal to:

To evaluate the given radical expression, we solve sequentially starting from the innermost square root:
1. Evaluate the innermost radical term:

$$\sqrt{144}=12$$

2. Substitute this value back into the expression:

$$\sqrt{248+\sqrt{52+12}}=\sqrt{248+\sqrt{64}}$$

3. Evaluate the next inner square root:

$$\sqrt{64}=8$$

4. Substitute this value back into the expression:

$$\sqrt{248+8}=\sqrt{256}$$

5. Calculate the final outer square root value:

$$\sqrt{256}=16$$