# Square Numbers(KS2, Year 6)

## The Lesson

A 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.
Note: 2 × 2 can be written 22 ("2 squared").

## Dictionary Definition

The Oxford English Dictionary defines a square number as "the product of a number multiplied by itself."

## The Square Numbers

The 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 Numbers

Finding 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  ## Square Numbers in Algebra

In 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 × x
Note: 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 Integers

Square 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 Positive

A 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 Number

The 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.

## Square Roots

If 2² = 4, then 4 is the square of 2. The inverse of the square is the square root, denoted by the √ symbol. 2 is the square root of 4, or √4 = 2.
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