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To prove root 2 is irrational

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To prove root 2 is irrational

Posted by Amishi Agarwal 1 year, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

B 01 Rojalin Behera 1 year, 6 months ago

Let assume that √2 is rational So, √2=a/b (a and b are positive co-prime number and b is not equal to 0) i.e. HCF (a,b)=1 b√2=a Squaring both the sides, we get (b√2)^2=a^2 =2b^2=a^2....(i) =b^2=a^2/2 =a^2/2 (if P is a prime number, if P divides a^2 then P divides a) =a/2 So, a=3c for some integer c Putting a=2c in equation (i) 2b^2=(2c)^2 =2b^2=4c^2 =b^2=2c^2 =b^2/2=c^2 =b^2/2 (If P is a prime number, if P divides a^2 then P divides a) =b/2 So, a and b have another prime factor 2 But this contradicts the fact that a and b are co-prime number. This contradiction has arisen due to our incorrect assumption. So, √2 is an irrational number. Hence, proved.

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