Why “squared”?
A number times itself is a square of tiles.
Why “square”?
The numbers 1, 4, 9, 16, 25, … are called square numbers.
Why do you think they are called squares?
What this lesson covers
The idea
A square number is the product of a number with itself; for any number n, including fractions and decimals, n × n is written n², read 'n squared', and is the area of a square of side n.
Why “square”?
The numbers 1, 4, 9, 16, 25, … are called square numbers.
Why do you think they are called *squares*?
- That many tiles can be laid out as a square
- They are all even numbers
- Nobody knows
Build squares
Drag the orange corner (or tap − and +). Count the tiles in every square you make.
n × n = n²
A square number is a number times itself: n × n = n², read “n squared”. It is the area of a square of side n.
The side does not have to be a whole number. A side of 2.5 splits the square into four parts:
A side of 3/5 is part of a unit square cut into 5 × 5 = 25 small squares. The shaded part is 3 × 3 = 9 of them.
- Side | Tiles | Written
- 1 | 1 × 1 = 1 | 1²
- 2 | 2 × 2 = 4 | 2²
- 3 | 3 × 3 = 9 | 3²
- 4 | 4 × 4 = 16 | 4²
- 5 | 5 × 5 = 25 | 5²
Notes
A square number is a number times itself: n × n = n², the area of a square of side n. This works for fractions and decimals too.
Check yourself
What does 7² mean?
A square tile has side 12 cm. What is its area?
Answer: 144 sq cm
12 × 12 = 144, so 12² = 144 sq cm.
What is 1.5²?
Answer: 2.25
1.5 × 1.5 = 2.25.
What is (2/3)²?
- 7 × 2 = 14. 14 is 7 doubled. Squared means 7 times itself.
- 7 × 7 = 49 — correct. Yes! 7² = 7 × 7 = 49, the number of tiles in a 7 by 7 square.
- 7 + 7 = 14. Adding 7 to itself gives 14. Squaring multiplies: 7 × 7.
- 72. The little 2 is not a digit next to the 7. It says “multiply 7 by itself”.
- 4/9 — correct. Yes! (2/3)² = 2/3 × 2/3 = 4/9. Top × top and bottom × bottom.
- 4/6. You squared only the top. The bottom is multiplied by itself too: 3 × 3 = 9.
- 2/9. You squared only the bottom. The top is multiplied by itself too: 2 × 2 = 4.