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solve root 2 is an irrational number

Posted by Dev Pc 4 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Akash Boominathan 4 years, 6 months ago

Let us assume that √2 is rational such that p and q are coprimes and q not equal to 0 Therefore, √2 = p/q => √2q = p , SQUARING ON BOTH SIDES : 2q^2 = p^2 , 2 divides p^2 therefore 2 divides p__________(1) Let us take p = 2r for an integer r Therefore, => 2q^2 = (2r)^2 => q^2 = 2r^2 2 divides q^2 therefore it also divides q __________(2) From (1),(2) It shows that p and q have 2 as common factor, but it contradicts the fact that p and q are coprimes. This contradiction has arisen due to our wrong assumption. Therefore, we conclude that √2 is irrational //

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CBSE > Class 10 > Mathematics