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Show that 5-root3 is a irrational …

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Show that 5-root3 is a irrational number

    • Posted by Chinmaya Senapati 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    We will solve this by contradiction method i.e., 

    Assume {tex}5 - \sqrt { 3 } = \frac { p } { q }{/tex} be a rational number.
    {tex}\therefore 5 - \frac { p } { q } = \sqrt { 3 }{/tex} or {tex}\frac { 5 q - p } { q } = \sqrt { 3 }{/tex},
    Since p,q are integers, therefore {tex}\frac { 5 q - p } { q }{/tex} is a rational number, which is a contradiction,since {tex}\sqrt 3{/tex} is an irrational number.
    Therefore, our supposition is wrong and hence, 5 - {tex}\sqrt 3{/tex} is irrational.

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