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Let us assume that for some positive integer n, is rational.
, where p and q are positive integers and
Applying identity :- (a+b)^2= a^2 + b^2 + 2ab
Now, we see that p^2 can be divided by 2, then p can be divided by 2.
Let p=2a.
Now, q^2 is divisible by 2, then q is also divisible by 2.
Therefore, are pre assumption is contradicted, and so there is no positive integer n, for which is rational.
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