Prove that is an irrational number.
Suppose is not an irrational number, then it must be a rational number.
So let =q where q is a rational number.
So here we have an equation with its left side is a rational number(as the set of rational numbers is closed under subtraction and division i.e the subtraction and division of two rational numbers is always a rational number)and so its right side must also be a rational number.
is a rational number
Which is a contradiction. So our basic assumption must be wrong.
=q where q is a rational number,is wrong
is an irrational number.
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