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√5 is irrational .prove (3-√5)is irrational |
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Answer» Let 3-_/5 be rational and co prime 3-_/5=a/b Therefore,3- a/b=_/5 _/5 = 3-a/b = 3b - a/bSince a and b are integers , we get 3 - a/b is rational, and so _/5 is rationalBut this contradicts the fact that _/5 is irrational.This contradiction has arison because of our incorrect assumption that 3 -_/5 is rational.So, we conclude that 3-_/5 is irrational. See in ncert book in chapter 1examples |
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