InterviewSolution
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InterviewSolution
| 1. |
prove that underoot 3is rational |
| Answer» Let us assume on the contrary that root 3 is a Rational Number. Then , there exists co-prime positive integers a and b such thatUnder root 3 =a/bOn Squaring both sides, We get a^2= 3b^2---------------(¡)=> 3|a^2=>3|a-------------------(ii)Let a= 3c , for some integer ca^2=9c^2 [ On Sq. Both sides ]=>3b^2 =9c^2 [From (¡) ]=>b^2= 3c^2=> 3|b^2=>3|b-------------------(¡¡¡)From (ii) and (¡¡¡ ), We get , that 3 is a common factor of both a and b.This contradicts the fact that a and b are co-primes [i.e. their H.C.F. is 1].So , Our Assumption is incorrect. Hence,Underroot 3 is an irrational number. [PROVED] | |