2. Prove that
is irrational.
Solution:
We will prove this by contradiction. Lets suppose that
is rational. It means that we have co-prime integers a and b
such that
(1)
a and b are integers. It means L.H.S of (1) is rational but we know that
is irrational (See Proof). It is not possible. Therefore, our supposition is wrong.
cannot be rational. Hence,
is irrational.
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