# 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

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## 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

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## 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.