"prove that 7√5 is irrational number"
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Because a, b, and 7 are integers 7b−ab is rational, implying that √5 is rational. But this contradicts with the fact that √5 is irrational. The contradiction is because of the incorrect assumption that 7 - √5 is rational. ∴ We can conclude that 7 - √5 is irrational.
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