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Prove that if $a$ is an integer and not a square number then $\sqrt a$ is 
irrational.

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NOTES AND BACKGROUND<br></br>
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You may have seen a proof that the square root of 2 is irrational and you can 
look this up in most textbooks written for students in their last year of 
school mathematics or first year of university mathematics. \par

It is just as easy to prove that if $a$ is not a square number then 
$\sqrt a$ is irrational.
\par
First prove that if $a$ is a natural number and $\sqrt a $ is rational then 
it is a 
square number (an integer $n^2$ for some integer $n$.) 
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