The strategy
How it works
Read n² as n × n, not n × 2.
Recall or build the matching multiplication fact.
Use the growing pattern between neighboring squares to check.
See it in action
Worked examples
Example 16²
- A square means 6 × 6.
- Six groups of six make 36.
- So 6² = 36.
Answer: 36
Example 29²
- 9 × 9.
- Think 10 × 9 = 90, then take away 9.
- 90 − 9 = 81.
Answer: 81
A quick heads-up
Common mistakes to avoid
- Reading 7² as 7 × 2; the small raised 2 means multiply the number by itself.
- Confusing a square number with its square root; 36 is 6², while 6 is its root.
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 does 5² mean?
The exponent 2 means multiply the base by itself: 5 × 5.
What is 7²?
7² = 7 × 7 = 49.
Which number is a perfect square?
25 = 5 × 5, so 25 is a perfect square.
Keep the momentum
Try a few practice problems
Choose a comfortable range and work through a short round with the free mental math trainer.