Prove that root 11is an irrational number

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Prove that root 11is an irrational number

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Nevaeh 1 month 2021-08-13T11:59:23+00:00 1 Answer 0 views 0

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    2021-08-13T12:01:11+00:00

    Let as assume that √11 is a rational number.

    A rational number can be written in the form of p/q where q ≠ 0 and p , q are non negative number.

    √11 = p/q ….( Where p and q are co prime number )

    Squaring both side !

    11 = p²/q²

    11 q² = p² ……( i )

    p² is divisible by 11

    p will also divisible by 11

    Let p = 11 m ( Where m is any positive integer )

    Squaring both side

    p² = 121m²

    Putting in ( i )

    11 q² = 121m²

    q² = 11 m²

    q² is divisible by 11

    q will also divisible by 11

    Since p and q both are divisible by same number 11

    So, they are not co – prime .

    Hence Our assumption is Wrong √11 is an irrational number .

    I hope it will help you…..☺️

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