Prove that there is no rational number whose square is 2 :

“Prove that there is no rational number whose square is 2.” This type of proof is
(a) proof by contraposition
(b) direct proof
(c) proof by contradiction
(d) proof by counter-example

Anurag Mishra Professor Asked on 23rd February 2016 in Science.
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    Answer: (c)  proof by contradiction 

    Solution:-
    Given-
    √2 = m/n
    where n and m are relatively prime, reduced to simplest form.
    Clearly then, m cannot be even.

    Square both sides:
    2 = m² / n²
    2 n² = m²

    m² is even, so m must also be even.

    Therefore assumption is false, and √2 cannot be expressed as a ratio of relatively prime integers so √2 is irrational, whose square is 2.

    Anurag Mishra Professor Answered on 25th February 2016.
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