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.


Want to learn more about number sequences? Click here.


For other related topics click:

Square roots

Cube numbers

Cube roots


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