Question

prove that ✓2+✓3 is irrational​

Answer 1

Let as assume that √2 + √3 is a rational number .

Then , there exists co - prime positive integers p and q such that

$\sqrt{2} + \sqrt{3} = \frac{p}{q} \\ \frac{p}{q} - \sqrt{3} = \sqrt{2} \\ sq \: on \: both \: side \\ ( \frac{p}{q} - \sqrt{3} {)}^{2} = \sqrt{2} {}^{2} \\ after \: solving \: \sqrt{3} \: is \: answer$

This contradicts the fact that √3 is irrational .

so assumption was incorrect . Here √2 + √3 is irrational.