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prove that underoot 3is rational

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prove that underoot 3is rational

Posted by Amit Saini 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Rushtam Chakraborty 7 years, 6 months ago

Let us assume on the contrary that root 3 is a Rational Number. Then , there exists co-prime positive integers a and b such that Under root 3 =a/b On Squaring both sides, We get a^2= 3b^2---------------(¡) => 3|a^2 =>3|a-------------------(ii) Let a= 3c , for some integer c a^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]

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CBSE > Class 10 > Mathematics