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If √2 is an rational number

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If √2 is an rational number

Posted by Visalraj Neelanchery 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Kaviya Sri Kanniappan 6 years, 5 months ago

Assume √2 as rational √2 = a/b ( where a and b are co- prime) co-prime - no's having 1 as common factor Squaring on both sides 2 = a^2/b^2 2b^2 = a^2----1 2 divides a^2 & a also a = 2 c Squaring on both sides a^2 = 4c^2----2 From 1 & 2 2b^2 = 4c^2 b^2 = 2c^2 b^2/2 = c^ 2 This shows 2 divides b^2 & b also Hence 2 is a common factor for a and b,this contradicts the fact that a and b are co- prime.so,our assumption is wrong. Therefore, √2 is Irrational.

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