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Prove √2 is irrational.

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Prove √2 is irrational.

    • Posted by Akash K 5 years ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years ago

    Let us assume √2 is rational number.
    a rational number can be written into he form of p/q
    √2=p/q
    p=√2q
    Squaring on both sides
    p²=2q²__________(1)
    .·.2 divides p² then 2 also divides p
    .·.p is an even number
    Let p=2a (definition of even number,'a' is positive integer)
    Put p=2a in eq (1)
    p²=2q²
    (2a)²=2q²
    4a²=2q²
    q²=2a²
    .·.2 divides q² then 2 also divides q
    Both p and q have 2 as common factor.
    But this contradicts the fact that p and q are co primes or integers.
    Our supposition is false
    .·.√2 is an irrational number.

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