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| 1. |
Prove that 7√5 are irrational |
| Answer» We can prove\xa0{tex}7 \\sqrt { 5 }{/tex} irrational\xa0by contradiction.Let us suppose that {tex}7 \\sqrt { 5 }{/tex} is rational.It means we have some co-prime integers a and b (b≠ 0)such that{tex}7 \\sqrt { 5 } = \\frac { a } { b }{/tex}{tex}\\Rightarrow \\sqrt { 5 } = \\frac { a } { 7 b }{/tex}\xa0.......(1)R.H.S of (1) is rational but we know that{tex}\\sqrt { 5 }{/tex}is irrational.It is not possible which means our supposition is wrong.Therefore, {tex}7 \\sqrt { 5 }{/tex} cannot be rational.Hence, it is irrational. | |