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Prove that Root 5 irrational

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Prove that Root 5 irrational

    • Posted by Rajendar Ray 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Prince Raj 6 years, 4 months ago

    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)² 5=a²/b² a²=5b²_(¹) Clearly,5 is a factor of a² Then 5 is also a factor of a. a=5m On squaring both sides, a²=(5m)² a²=25m² 5b²=25m²[From eq(¹)] b²=5m² Clearly,5 is a factor of b² 5 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)

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