Only the last digit matters
The last digit of n tells the last digit of n².
29 squared
21² = 441 and 31² = 961. Both numbers end in 1, and so do both squares.
The number 29 ends in 9. What will 29² end in?
What this lesson covers
The idea
A number with 1 or 9 in the units place has a square ending in 1, and a number with 4 or 6 in the units place has a square ending in 6.
29 squared
21² = 441 and 31² = 961. Both numbers end in 1, and so do both squares.
The number 29 ends in 9. What will 29² end in?
- 9
- 1
- 8
Fill the cards
Tap numbers to square them. Each card remembers the last digit of the squares. Fill the four highlighted cards — two numbers each.
Why only the last digit?
A number with 1 or 9 in the units place has a square ending in 1. A number with 4 or 6 in the units place has a square ending in 6.
When we multiply, the last digit of the answer comes only from (last digit) × (last digit):
- Number ends in | Last digits multiplied | Square ends in
- 1 | 1 × 1 = 1 | 1
- 9 | 9 × 9 = 81 | 1
- 4 | 4 × 4 = 16 | 6
- 6 | 6 × 6 = 36 | 6
Notes
A number ending in 1 or 9 has a square ending in 1; a number ending in 4 or 6 has a square ending in 6.
Check yourself
What is the last digit of 49²?
Answer: 1
49 ends in 9, and 9 × 9 = 81, so 49² ends in 1. (49² = 2401.)
Which of these squares ends in 6?
Which number has a square that ends in 1?
- 13². 13 ends in 3 and 3 × 3 = 9, so 13² ends in 9 (169).
- 24² — correct. Yes! 24 ends in 4 and 4 × 4 = 16, so 24² ends in 6 (576).
- 35². 35 ends in 5 and 5 × 5 = 25, so 35² ends in 5 (1225).
- 17². 17 ends in 7 and 7 × 7 = 49, so 17² ends in 9 (289).
- 22. 22 ends in 2 and 2 × 2 = 4, so 22² ends in 4.
- 39 — correct. Yes! 39 ends in 9 and 9 × 9 = 81, so 39² ends in 1 (1521).
- 53. 53 ends in 3 and 3 × 3 = 9, so 53² ends in 9.
- 67. 67 ends in 7 and 7 × 7 = 49, so 67² ends in 9.