Can the expression √n+√m be rational if neither n,m∈N are perfect squares? It doesn't seem likely, the only way that could happen is if for example √m=a−√n, a∈Q, which I don't think is possible, but how to show it?
Answer
Squaring we get, m=a2+n−2a√n⟹√n=a2+n−m2a which is rational
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