Question

prove that 2√3 is irrational​

Answer 1

$\huge\text{\underline{Answer}}$

Let $\</strong><strong>2 \sqrt{3} </strong><strong>$ be a rational number then,it can be written in the form of $</strong><strong>\frac{p}{q} </strong><strong>$ where p and q are co-prime and q ≠ 0.

Then,

$2 \sqrt{3} = \frac{p}{q}$

Sift 2 on R. H. S

$\sqrt{3} = \frac{p}{2q}$

We know that every operation of rational is a rational number.

Also division of rational number is a rational number .

here, L. H. S. is an irrational number but R. H. S is a rational number .

I. e, L. H. S ≠ R. H. S

hence, our supposition is wrong

$\2 \sqrt{3}$ is an irrational number.