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Prove that √7 is an irrational |
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Answer» Answer: Step-by-step EXPLANATION: √7 = p / q √7 x q = p squaring on both sides 7q² = p² ------1. p is divisible by 7 p = 7c [c is a POSITIVE integer] [squaring on both sides ] p²= 49c² subsitute p² in eqn(1) we get 7q² = 49 c² q² = 7c² q is divisble by 7 thus q and p have a common factor 7. there is a contradiction to our assumption as our assumsion p & q are co prime but it has a common factor. so that √7 is an IRRATIONAL. |
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