√(248 + √(51 + √169)) = ?
2024
√(248 + √(51 + √169)) = ?
- A.
12
- B.
16
- C.
15
- D.
18
Attempted by 8 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
To evaluate nested square roots, start from the innermost expression and work your way outward.
Evaluate the innermost square root:
The expression is sqrt(248 + sqrt(51 + sqrt(169))).
sqrt(169) = 13.
Simplify the next level:
Now the expression is sqrt(248 + sqrt(51 + 13)).
51 + 13 = 64.
sqrt(64) = 8.
Final calculation:
Now the expression is sqrt(248 + 8).
248 + 8 = 256.
sqrt(256) = 16.