Show that there is no positive integer ‘n’ for which √ −1 + √ + 1 is rational
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∵√n−1 is also a perfect square of positive integers. Thus we can say that √n+1 and √n−1 are perfect squares of positive integers. It contradicts the fact that two perfect squares differ by 3. Thus there is no positive integer n for which √n−1+√n+1 is rational.
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