Number System — Evaluate the square exactly: 1307 × 1307. Choose the correct value.

Introduction / Context:
Squaring a four-digit number can be handled accurately using algebraic expansion. Noticing that 1307 is near 1300 enables a near-base method to reduce effort and organize calculations cleanly.

Given Data / Assumptions:

• We must compute 1307^2 exactly.
• Use place-value or near-base expansions for reliability.
• All arithmetic steps should be double-checked to avoid transposition errors.

Concept / Approach:
Write 1307 = 1300 + 7. Then (1300 + 7)^2 = 1300^2 + 2*1300*7 + 7^2. This standard expansion separates the problem into manageable parts and minimizes mental load.

Step-by-Step Solution:
1) Compute 1300^2 = (13^2) × 100^2 = 169 × 10000 = 1,690,000.2) Compute 2*1300*7 = 2600*7 = 18,200.3) Compute 7^2 = 49.4) Sum: 1,690,000 + 18,200 + 49 = 1,708,249.

Verification / Alternative check:
Direct multiplication (1307 × 1307) will yield the same 1,708,249. Checking the last two digits: 07 × 07 ends with 49, matching the result's ending 49, which is a good quick sanity check.

Why Other Options Are Wrong:
1601249, 1607249, 1609209 are too small (they ignore the growth from adding 7 to 1300 twice). 1701249 is short by 7000 compared to the correct middle term contribution.

Common Pitfalls:
Forgetting the 2ab middle term; miscomputing 1300^2; dropping zeros when handling 10000 multipliers; transposing digits when adding the parts.

Final Answer:
1708249