Solve by approximation: 36.0001 ÷ 5.9998 × √(?) ≈ 108.0005. Find the best matching value of ? from the options.

Introduction / Context:
We have a near-integer structure: 36 ÷ 6 × √(?) ≈ 108. The tiny decimal perturbations suggest using close-by integers, then picking the option that best reproduces the target 108.0005.

Given Data / Assumptions:

• Expression: (36.0001 ÷ 5.9998) × √(?) ≈ 108.0005.
• 36.0001 ÷ 5.9998 ≈ 6 (very close).
• We must select ? from the given options.

Concept / Approach:
Approximate the prefactor as 6. Then 6 * √(?) ≈ 108 ⇒ √(?) ≈ 18 ⇒ ? ≈ 324. Since 324 is not an option, choose the nearest option whose square root is closest to 18.

Step-by-Step Solution:

Verification / Alternative check:
If we retain the more precise factor (36.0001/5.9998 ~ 6.0001…), the product with √325 falls even closer to 108.0xx, validating 325 as the best fit among the options.

Why Other Options Are Wrong:

• 18 or 16: These look like √(?) candidates, but the question asks for ? itself.
• 256: √256 = 16, giving about 96 (too small).

Common Pitfalls:
Answering with the square root instead of the radicand, or ignoring the approximation context and insisting on an unavailable exact 324. In approximation sets, select the closest viable option.

Final Answer: