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InterviewSolution
| 1. |
Root 5 irrational |
| Answer» Let\xa0{tex}\\sqrt 5{/tex}\xa0is a rational number.{tex}\\sqrt { 5 } = \\frac { a } { b }{/tex}(a, b are co-primes and b{tex}\\neq{/tex}0)or,\xa0{tex}a = b \\sqrt { 5 }{/tex}On squaring both the sides, we get\xa0a2=5b2 ---------------------------------(1)Hence 5 is a factor of a2so 5 is a factor of aLet a = 5c, (c is some integer){tex}\\therefore{/tex}\xa0a2\xa0= 25c2\xa0From equation(1) putting the value of a2or, 5b2\xa0= 25c2or b2=5c2so 5 is a\xa0factor of b2or 5 is a factor of bHence 5 is a common factor of a and bBut this contradicts the fact that a and b are co-primes.This is because we assumed that\xa0{tex}\\sqrt 5{/tex}\xa0is rational{tex}\\therefore{/tex}\xa0{tex}\\sqrt 5{/tex}\xa0is irrational. | |