Question

prove that 2 root 3_ 1 is irrational

Answer 1

If we add ( 3 + 2 ) + ( 3 − 2 ) we get which is irrational. But the sum of two rationals can never be irrational, because for integers a , b , c ,
which is rational. Therefore, our assumption that is rational is incorrect, so is irrational.

Answer 2

$2 \sqrt{3} - 1$
to prove this irrational ,we first assume it is rational,so it can be represented in p/q form,where p and q are coprime number.
$2 \sqrt{3} - 1 = \frac{p}{q} \\ 2 \sqrt{3} = \frac{p}{q} + 1$
$2 \sqrt{3} = \frac{p + q}{q} \\ \sqrt{3 } = \frac{p + q}{2q}$

here √3 equal to the form p/q,but we know that √3 is an irrational number,so due to conflicts we say that we wrongly assumed that number rational,since we prove that given number it irrational.