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Prove that √2 is an irrational

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Prove that √2 is an irrational

    • Posted by Prasoon Thakur 6 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 6 years, 3 months ago

    Given √2 is irrational number.
    Let √2 = a / b wher a,b are integers b ≠ 0
    we also suppose that a / b is written in the simplest form
    Now √2 = a / b ⇒ 2 = a2 / b2 ⇒   2b2 = a2
    ∴ 2b2 is divisible by 2
    ⇒  a2 is divisible by 2    
    ⇒  a is divisible by 2  
    ∴ let a = 2c
    a2 = 4c2 ⇒ 2b2 = 4c2 ⇒ b2 = 2c2
    ∴ 2c2  is divisible by 2
    ∴ b2  is divisible by 2
    ∴ b  is divisible by 2
    ∴a are b   are  divisible by 2 .
    this contradicts our supposition that a/b is written in the simplest form
    Hence our supposition is wrong
    ∴ √2 is irrational number.

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