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Prove that √3 is irrational no.

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Prove that √3 is irrational no.

Posted by Priyanshu Sahu 2 years ago

CBSE > Class 10 > Mathematics

3 answers

Priya Mahajan 2 years ago

On contrary, let's assume √3 is rational So we can write it as of p/q where q is not equal to zero. Suppose p and q have a common factor other than 1, so on dividing it by that factor we get √3 = a/b , where a and b are coprime. So a = √3b -----(I) Squaring both sides, we get, a^2= 3b^2 So a^2 is divisible by 3 => a is divisible by 3 => a =3c Substitute in (i), we get, 3c=√3b => 9c^2= 3b^2 => 3c^2= b^2 => b^2 is divisible by 3 So b is divisible by 3 So, a and b have at least 3 as common factor But this contradicts that a and b are coprime So our assumption is wrong So √3 is irrational.

Saraswati Kumari 2 years ago

Yes it is irrational

Simran Singh 2 years ago

Yes it's a irrational number

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