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Prove that Root 5 irrational |
| Answer» If possible,Let √5 be rational√5=a/b where a and b are integers and co-prime.On squaring both sides,(√5)²=(a/b)²5=a²/b²a²=5b²_(¹)Clearly,5 is a factor of a²Then 5 is also a factor of a.a=5mOn squaring both sides,a²=(5m)²a²=25m²5b²=25m²[From eq(¹)]b²=5m²Clearly,5 is a factor of b²5 is a factor of b.Here,a and b are integers where 5 is a factor of both the integers.So,there is a contradiction arisened 5 is not a co-prime no.Hence,√5 is irrational (By contradiction method) | |