The second power of an integer: 0, 1, 4, 9, 16, 25... are perfect squares.
A perfect square is a number we get when we multiply an integer by itself.
For example:
- 1 × 1 = 1
- 2 × 2 = 4
- 3 × 3 = 9
- 4 × 4 = 16
- 5 × 5 = 25
The numbers 1, 4, 9, 16, and 25 are all perfect squares because they are the result of squaring an integer.
We can also write perfect squares using exponents:
- 3² = 9
- 6² = 36
Perfect squares are closely connected to square roots. If 25 is a perfect square, then √25 = 5.
We use perfect squares when:
- Finding the area of a square
- Working with square roots
- Solving quadratic equations
When Do Students Learn About Perfect Squares?
Students begin learning about perfect squares when they study multiplication and exponents.
Grades 4–5 – Introduction to Squaring Numbers
Students recognize square numbers through multiplication facts and area models.
Grades 6+ – Using Perfect Squares in Algebra
Students use perfect squares when working with exponents, square roots, and solving equations.
