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Prove that √7 is irrational

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Prove that √7 is irrational

    • Posted by Amarkanta Meitei 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Amarkanta Meitei 6 years, 9 months ago

    Let us assume that √7 be rational Then it must in the form of p/q (q#0) { p and q are co-prime } √7=p/q => √7 × q=p Quiring on both sides => 7q2 = p2 ------->(1) p2 is divisible by 7 p is divisible by 7 p=7c (c is a positive integer) (squaring on both side) p2=49c2--------> (2) substitute p2 in equipment (1) we get 7q2=49c2 =>q is divisible by 7 Thus q and p have a common factor 7 there is a contradiction as our assumption p&q are co-prime but it has a common factor So that √7 is an irrational.

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