Evaluate :
`sqrt(248 + sqrt(52 + sqrt(144)))`

Answer

To evaluate the expression \( \sqrt{248 + \sqrt{52 + \sqrt{144}}} \), we will simplify it step by step.

### Step 1: Simplify \( \sqrt{144} \)
We know that:
\[ \sqrt{144} = 12 \]
So we can rewrite the expression as:
\[ \sqrt{248 + \sqrt{52 + 12}} \]

### Step 2: Simplify \( \sqrt{52 + 12} \)
Now, calculate \( 52 + 12 \):
\[ 52 + 12 = 64 \]
Thus, we have:
\[ \sqrt{52 + 12} = \sqrt{64} = 8 \]
Now, we can rewrite the expression again:
\[ \sqrt{248 + 8} \]

### Step 3: Simplify \( 248 + 8 \)
Next, calculate \( 248 + 8 \):
\[ 248 + 8 = 256 \]
So now we have:
\[ \sqrt{256} \]

### Step 4: Calculate \( \sqrt{256} \)
Finally, we know that:
\[ \sqrt{256} = 16 \]

### Final Answer
Thus, the value of \( \sqrt{248 + \sqrt{52 + \sqrt{144}}} \) is:
\[ \boxed{16} \]