Approximate total: (15.96)^2 + 75% of 285 ≈ ?

Introduction / Context:
This combines a squared decimal with a percentage of an integer. We compute each part accurately enough to pick the closest integer option.

Given Data / Assumptions:

• (15.96)^2.
• 75% of 285 = 0.75 * 285.

Concept / Approach:
Calculate the square carefully, compute the percentage exactly, add them, and then round to the nearest choice if needed.

Step-by-Step Solution:

Verification / Alternative check:
Rounding the square to 255 would give 255 + 213.75 = 468.75, still near 470 and far from the other options, strengthening the choice of 470.

Why Other Options Are Wrong:

• 435 or 440: Too low relative to ≈468.5.
• 485: Slightly high; our total is well under 480.

Common Pitfalls:
Approximating the square too coarsely (e.g., using 16^2 = 256 without recognizing the small reduction from 16 to 15.96), which can introduce a larger rounding error. Compute the square or use a close estimate like 16^2 minus a small correction.

Final Answer: