The value of the given expression

To evaluate a nested radical expression, always resolve the innermost square root first, substitute its exact value into the radical that contains it, and repeat outward — the outer square roots depend on the inner ones being simplified first; they cannot be combined before that.

1. Evaluate the innermost square root: √144 = 12.

2. Substitute this value into the middle sum: 52 + 12 = 64.

3. Evaluate the middle square root: √64 = 8.

4. Substitute this value into the outer sum: 248 + 8 = 256.

5. Evaluate the outer square root: √256 = 16.

Check by squaring back from the answer: 162 = 256 = 248 + 8, and 82 = 64 = 52 + 12, and 122 = 144 — every layer of the nested radical matches, confirming 16 is correct.