Show that 5-root3 is a irrational number

1.	Show that 5-root3 is a irrational number
Answer» We will solve this by contradiction method i.e.,\xa0Assume\xa0{tex}5 - \\sqrt { 3 } = \\frac { p } { q }{/tex}\xa0be a rational number.{tex}\\therefore 5 - \\frac { p } { q } = \\sqrt { 3 }{/tex}\xa0or\xa0{tex}\\frac { 5 q - p } { q } = \\sqrt { 3 }{/tex},Since p,q are integers, therefore\xa0{tex}\\frac { 5 q - p } { q }{/tex} is a rational number, which is a contradiction,since\xa0{tex}\\sqrt 3{/tex} is an irrational number.Therefore, our supposition is wrong and hence, 5 - {tex}\\sqrt 3{/tex}\xa0is irrational.

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