The value of the given expression
2013
The value of the given expression
Answer: C. 16 — To evaluate a nested radical expression, always resolve the innermost square root first, substitute its exact value into the radical that contains it, and…
- A.
14
- B.
12
- C.
16
- D.
13
Attempted by 3 students.
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Correct answer: C
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.
Evaluate the innermost square root: √144 = 12.
Substitute this value into the middle sum: 52 + 12 = 64.
Evaluate the middle square root: √64 = 8.
Substitute this value into the outer sum: 248 + 8 = 256.
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.