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Prove √2is irrational

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Prove √2is irrational

    • Posted by Pabi Hadisda 1 year, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sakshi Kolekar 1 year, 5 months ago

    Let , √2 is rational number √2=a,b(a,b,are coprime) √2b=a Squaring on both sides (√2b²)=a² 2b²=a²—1 b²=a²/2 'a²'is divisible by '2' 'a' is divisible by '2' a/2=m a=2m Putting in eq 1 2b²=a² 2b²=(2m)² 2b²=4m² b²=4m²/2 b²=2m² b²/2=m² m²= b²/2 'b²'is divisible by '2' 'b'is divisible by '2' But,a and b are coprime Our assumption was wrong Therefore, √2 is irrational number

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