Approximate (nearest sensible option): 36.98276421 × 21.00002 = ?

Introduction:
Products with one factor near an integer multiple lend themselves to quick rounding. Because 36.98… is close to 37 and 21.00002 is essentially 21, the result should be near 37 × 21, with negligible adjustment from tiny decimals.

Given Data / Assumptions:

• First factor ≈ 37
• Second factor ≈ 21
• Options are spaced by 10 or more, so coarse rounding suffices.

Concept / Approach:
Compute 37 × 21 = 777. Adjust slightly downward because the first factor is a bit below 37 (36.98…) while the second is a hair above 21. The net effect keeps the product near 777, closer to 775 than 785.

Step-by-Step Solution:

Verification / Alternative check:
Exact multiplication (calculator) would yield about 776.64, which is 1.64 away from 775 and 8.36 from 785. Hence 775 is nearest.

Why Other Options Are Wrong:
785, 800, and 805 are too large; 770 is slightly farther than 775 from the refined estimate.

Common Pitfalls:
Over-correcting for the tiny 0.00002 in the second factor; its impact is orders of magnitude smaller than the integer parts.

Final Answer:
775