The strategy
How it works
Choose a nearby round base.
Find the offset between the number and the base.
Calculate base² + 2 × base × offset + offset².
See it in action
Worked examples
Example 112²
- Use 10 + 2.
- 10² + 2 × 10 × 2 + 2².
- 100 + 40 + 4 = 144.
Answer: 144
Example 219²
- Use 20 − 1.
- 20² − 2 × 20 × 1 + 1².
- 400 − 40 + 1 = 361.
Answer: 361
A quick heads-up
Common mistakes to avoid
- Adding only one base-times-offset term; the cross-term is doubled.
- Forgetting the offset squared, even when the offset is negative.
Your turn
Check your understanding
Choose an answer to see instant feedback and a short explanation. You can take the quiz again any time.
Question 1 of 3
What is 11²?
(10 + 1)² = 100 + 20 + 1 = 121.
What is 18² using 20 − 2?
400 − 80 + 4 = 324.
In (10 + 3)², what is the offset-squared part?
The offset is 3, and its square is 3² = 9.
Keep the momentum
Try a few practice problems
Choose a comfortable range and work through a short round with the free mental math trainer.