Approximate and solve: 1169.997 ÷ 18.001 + 7.0009 × 4.9898 ≈ √(?)

Introduction / Context:
The left-hand side is very close to 1169.997/18 + 7*5, which is near 65 + 35 = 100. Since the right side is a square root, we square the approximate total to select the matching radicand from options.

Given Data / Assumptions:

• Compute LHS: 1169.997 ÷ 18.001 + 7.0009 × 4.9898.
• Approximate denominators and multipliers to convenient integers.

Concept / Approach:
Approximate term-by-term, sum, then interpret the result as √(?) ≈ total. Square the total to find ? and match to the choices.

Step-by-Step Solution:

Verification / Alternative check:
Fine-grain: 1169.997/18.001 is slightly under 65 and 7.0009*4.9898 is slightly under 35, but the total still hovers extremely close to 100, validating 10000 as the best radicand choice.

Why Other Options Are Wrong:

• 99 or 100: These are values of the square root, not the radicand.
• 9000: Not a perfect square close to 100^2; √9000 ≈ 94.9, too small.

Common Pitfalls:
Stopping at the approximate total (100) and selecting 100 instead of squaring to obtain the underlying ?. Always map √(?) ≈ total back to the radicand.

Final Answer: