Squares of counting numbers
Perfect squares come from natural numbers.
Is 6.25 “perfect”?
1 × 1, 2 × 2, 3 × 3, … give 1, 4, 9, 16, 25, … These are called perfect squares.
But 2.5 × 2.5 = 6.25 is also a number times itself.
Is 6.25 a perfect square?
What this lesson covers
The idea
The squares of natural numbers are called perfect squares.
Is 6.25 “perfect”?
1 × 1, 2 × 2, 3 × 3, … give 1, 4, 9, 16, 25, … These are called perfect squares.
But 2.5 × 2.5 = 6.25 is also a number times itself.
Is 6.25 a perfect square?
- Yes
- No
- Only half of it
Perfect or not?
Tap a chip, then tap its box. Ask: *is it a natural number times itself?*
Natural number times itself
The squares of natural numbers are called perfect squares: 1, 4, 9, 16, 25, …
The sides 2.5 and 3/5 are not natural numbers. So 6.25 and 9/25 are squares, but not perfect squares.
- Natural number | Perfect square
- 1 | 1² = 1
- 2 | 2² = 4
- 3 | 3² = 9
- 4 | 4² = 16
- 5 | 5² = 25
- 10 | 10² = 100
Notes
The squares of natural numbers are called perfect squares: 1, 4, 9, 16, 25, …
A perfect square is the area of a square whose side is a whole number of units.
Check yourself
Which of these is a perfect square?
How many perfect squares are there from 1 to 50?
Answer: 7
1, 4, 9, 16, 25, 36, 49 — seven perfect squares.
What is the 15th perfect square?
Answer: 225
15 × 15 = 225.
- 0.49. 0.49 = 0.7 × 0.7, but 0.7 is not a natural number.
- 81 — correct. Yes! 81 = 9 × 9, and 9 is a natural number.
- 80. 8 × 8 = 64 and 9 × 9 = 81. Nothing times itself gives 80.
- 1/4. 1/4 = 1/2 × 1/2, but 1/2 is not a natural number.