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Proving sq.root(2) is irrational is a perfect instance.
Let us say, sq.root(2) a rational number.
x = sq.root(2) . y
x ^ 2 = 2 . y ^ 2 => proves x is even. let us further assume, x = 2 . z
4 z ^ 2 = 2 . y ^ 2 => y^2 = 2 . z^2 => proves y is even.
So, x and y are both even, which can be reduced further and further as proved above. So, x / y, representation of sq.root(2) doesn't exist, and hence irrational.
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