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Prove that `5-sqrt(3)`is an irrational number. |
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Answer» Let us assume that `5- sqrt3 `is a rational We can find co prime a & b `( b ne 0)` such that `5 - sqrt3= (a)/(b)` Therefore `5- (a)/(b) = sqrt3` So we get `(5b-a)/(b) = sqrt3` Since a & b are integers, we get `(5b-a)/(b)` is rational, and so `sqrt3` is rationa. But `sqrt3` is an irrational number Which contradicts our statement `therefore 5 - sqrt3` is irrational |
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