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: