Solve this multiple-choice question and choose the correct option.

Problem Restatement Calculate 13972 quickly without full long multiplication. Concept / Approach Use the identity (a − b)2 = a2 − 2ab + b2 with a = 1400 and b = 3. Step-by-Step Calculation 1397 = 1400 − 3(1400 − 3)2 = 14002 − 2 × 1400 × 3 + 32= 1,960,000 − 8,400 + 9 = 1,951,609 Verification Sanity check: 14002 = 1,960,000; the square should be slightly less — difference 8,391, consistent. Final Answer 1951609

Curioustab

Evaluate the square: 1397 × 1397.

Aptitude Numbers Difficulty: Medium

Choose an option

A

1951609
B

1951409
C

1949609
D

1947409
E

None of these

Answer

Correct Answer: 1951609

Explanation

Problem Restatement

Calculate 1397² quickly without full long multiplication.

Concept / Approach

Use the identity (a − b)² = a² − 2ab + b² with a = 1400 and b = 3.

Step-by-Step Calculation

1397 = 1400 − 3(1400 − 3)² = 1400² − 2 × 1400 × 3 + 3²= 1,960,000 − 8,400 + 9 = 1,951,609

Verification

Sanity check: 1400² = 1,960,000; the square should be slightly less — difference 8,391, consistent.