Show that 5-root3 is a irrational …
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Posted by Chinmaya Senapati 4 years, 8 months ago
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Sia ? 4 years, 8 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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