Perfect Squares in Mathematics

Perfect Squares

• Definition: A perfect square is an integer that can be expressed as the square of another integer.

List of Perfect Squares

1. 1² = 1
2. 2² = 4
3. 3² = 9
4. 4² = 16
5. 5² = 25
6. 6² = 36
7. 7² = 49
8. 8² = 64
9. 9² = 81
10. 10² = 100
11. 11² = 121
12. 12² = 144
13. 13² = 169
14. 14² = 196
15. 15² = 225
16. 16² = 256
17. 17² = 289
18. 18² = 324
19. 19² = 361
20. 20² = 400

Properties of Perfect Squares

• Always non-negative.
• The square root of a perfect square is an integer.
• The last digit of a perfect square can only be 0, 1, 4, 5, 6, or 9.
• The difference between consecutive perfect squares increases linearly (e.g., 1, 3, 5, 7,...).

Applications of Perfect Squares

• Used in geometry to calculate areas of squares.
• Important in algebra for factoring and solving quadratic equations.

Definition of Perfect Squares

• A perfect square is an integer that can be written as the square of an integer.

List of Perfect Squares

• 1 is a perfect square (1² = 1).
• 2 produces 4 (2² = 4).
• 3 results in 9 (3² = 9).
• 4 gives 16 (4² = 16).
• 5 squares to 25 (5² = 25).
• 6 yields 36 (6² = 36).
• 7 equals 49 (7² = 49).
• 8 results in 64 (8² = 64).
• 9 produces 81 (9² = 81).
• 10 squares to 100 (10² = 100).
• 11 results in 121 (11² = 121).
• 12 yields 144 (12² = 144).
• 13 equals 169 (13² = 169).
• 14 produces 196 (14² = 196).
• 15 results in 225 (15² = 225).
• 16 squares to 256 (16² = 256).
• 17 gives 289 (17² = 289).
• 18 results in 324 (18² = 324).
• 19 equals 361 (19² = 361).
• 20 results in 400 (20² = 400).

Properties of Perfect Squares

• Perfect squares are always non-negative.
• The square root of a perfect square is always an integer.
• The last digit of perfect squares can only be 0, 1, 4, 5, 6, or 9.
• Differences between consecutive perfect squares follow a linear pattern (1, 3, 5, 7,...).

Applications of Perfect Squares

• Essential in geometry for calculating the areas of squares.
• Key in algebra for factoring and solving quadratic equations.