The LessonA square number is a number that results from a number being multiplied by itself. For example,
- 1 is a square number. It is 1 × 1.
- 4 is a square number. It is 2 × 2.
- 9 is a square number. It is 3 × 3.
Dictionary DefinitionThe Oxford English Dictionary defines a square number as "the product of a number multiplied by itself."
The Square NumbersThe square numbers are:
In a number square, the square numbers are shaded below:
These are just the square numbers up to 100. There are infinitely many square numbers, they go on forever.
How to Find Square NumbersFinding square numbers is easy. Just multiply a number by itself. The first 10 square numbers are found by multiplying 1 by itself, then 2 by itself, as shown below.
Interactive Game on Square Numbers
- You are the fish.
- Pop the bubbles with square numbers to collect red hearts. You need five to win.
- If a bubble with a square number reaches the top, you will lose a red heart.
- Avoid the bubbles with non-square numbers. If you pop one, you will lose one of your three lives.
- Good luck!
- The fish moves to wherever you taptowards your mouse clicks. (Hint: The farther the distance, the faster it moves.)
Square Numbers in AlgebraIn algebra, letters are used instead of numbers. Just as we can square a number...
22 = 2 × 2 = 4...we can square a letter:
x2 = x × xNote: We would say x2 as "x squared", just like we would say 22 as "2 squared". Here are some examples of squared letters in algebra:
Quadratic equations have an x2 term:
Pythagoras theorem relates the square of the lengths of the sides of a right triangle to each other.
The image below shows the formula for Pythagoras theorem and the lengths of the sides a, b and c of a right triangle:
The area of a circle is related to the square of its radius.
The image below shows the formula for the area of a circle and the circle's radius, r:
Square Numbers Come from IntegersSquare numbers are the result of integers (whole numbers, not fractions) being multiplied by themselves. A square number will always be an integer.
Square Numbers Are Always PositiveA square number is always a positive number. They can never be a negative number. Negative numbers can be multiplied by themselves to give a positive square number:
−2 × −2 = (−2)2 = 4
"Squaring" a NumberThe verb which describes the operation of multiplying a number by itself (e.g. 6 × 6) is "to square". When we multiply a number be itself , we call this "squaring" a number. 6 × 6 = 62 (called "6 squared").
Why "Square" Numbers?A square number is a number times itself.
12 = 1 × 1 = 1 22 = 2 × 2 = 4 32 = 3 × 3 = 9 The squares go 1, 4, 9...A square with sides of length 1 has an area of 1.
A square with sides of length 2 has an area of 4.
A square with sides of length 3 has an area of 9.
The areas go 1, 4, 9... The square of a number and the area of a square with side lengths of that number are the same.