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| 1. |
Prove that 3 root3 divieded by 5 is irrational |
| Answer» Suppose\xa0{tex}\\frac { 3 \\sqrt { 3 } } { 5 }{/tex}\xa0be a\xa0rational number{tex}\\therefore \\frac { 3 \\sqrt { 3 } } { 5 } = \\frac { a } { b }{/tex}, a and b are co-prime, b{tex}\\ne{/tex}\xa00{tex}\\Rightarrow \\sqrt { 3 } = \\frac { 5 a } { 3 b }{/tex}{tex}5a\\ and\\ 3b{/tex} are integers and\xa0{tex}\\sqrt3{/tex}\xa0is irrational.{tex}\\frac { 5 a } { 3 b }{/tex}\xa0is rational.{tex}\\therefore \\sqrt { 3 } \\neq \\frac { 5 a } { 3 b }{/tex}{tex}\\therefore{/tex}\xa0Our supposition is wrong{tex}\\Rightarrow \\frac { 3 \\sqrt { 3 } } { 5 }{/tex}\xa0is an\xa0irrational number. | |