# Square numbers (perfect squares)

Square numbers are otherwise known as **perfect squares**.

Each square number is the square of a whole number - i.e. the product of multiplying a whole number by itself.

## The first perfect square is 1 ...

... and is produced by multiplying 1 by itself

**1 squared = 1² = 1 x 1 = 1**

*(remember **² means squared)*

It can be represented by a single dot

**●**

## The second perfect square is 4 ...

... and results from multiplying 2 by itself

**2 squared = 2² = 2 x 2 = 4**

It can be represented by a pattern comprising 2 dots by 2 dots

**● ●**

**● ●**

## The third perfect square is 9

Here's the calculation

**3 squared = 3² = 3 x 3 = 9**

and the dot pattern looks like this

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**● ● ****●**

**● ● ****●**

## Let's consider the next two square numbers

The fourth number is 16

**4 squared = 4² = 4 x 4 = 16**

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**● ● ****● ****●**

**● ● ****● ****●**

The fifth number is 25

**5 squared = 5² = 5 x 5 = 25**

**● ● ****● ****● ****●**

**● ● ****● ****● ****●**

**● ● ****● ****● ****●**

**● ● ****● ****● ****●**

**● ● ****● ****● ****● **

## Now work out the sixth to tenth perfect squares

See how your calculations compare to the following

**6 squared = 6² = 6 x 6 = 36**

**7 squared = 7² = 7 x 7 = 49**

**8 squared = 8² = 8 x 8 = 64**

**9 squared = 9² = 9 x 9 = 81**

**10 squared = 10² = 10 x 10 = 100**

i.e. the sixth to tenth numbers are 36, 49, 64, 81 and 100.

*These can be represented by patterns comprising 6 dots by 6 dots, 7 dots by 7 dots, 8 dots by 8 dots, 9 dots by 9 dots, and 10 dots by 10 dots respectively.*

## Now bringing everything together ...

... gives the first ten square Nºs in sequence

You can easily calculate the nth term in this sequence using the formula

**nth term = n²**

*Use the squared symbol x² on you calculator if you wish. For example, to work out the 11th term/square Nº, enter 11 then press the x² key - you may need to press a shift or 2nd function button to access x². Your calculator display should show 121.*

Want to learn more about number sequences? Click here.

For other related topics click:

Square roots

Cube numbers

Cube roots

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