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Prove that the sum of a …

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Prove that the sum of a rational number and an irrational numbet is always irrational

    • Posted by Vansh Singh 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    Let R and I are rational number and irrational number respectively.
    Assume that sum of R and I is a rational number and equal to P<u1:p></u1:p>

    So R + I =P<u1:p></u1:p>

    or I =P - R......., (1)<u1:p></u1:p>

    As P and R both are rational number so P - R is also a rational number.<u1:p></u1:p>

    Hence from (1) I is a rational number<u1:p></u1:p>

    But this contradict that I is an irrational number.<u1:p></u1:p>

    This contradiction has come because we assumed that R+ I is a rational number.<u1:p></u1:p>

    Therefore the sum of irrational number and rational number is always an irrational number.<u1:p></u1:p>

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