Question

Prove that 2+√3 is a irrational number

Answer 1

Let ,

2 + √3 Is an rational number

Thus ,

$\sf \hookrightarrow 2 + \sqrt{3} = \frac{p}{q} \\ \\\sf \hookrightarrow \sqrt{3} = \frac{p}{q} - 2 \\ \\ \sf \hookrightarrow \sqrt{3} = \frac{p - 2q}{q}$

Here, √3 is an irrational number but (p - 2q)/q is rational number

Since , Irrational ≠ rational

Thus , our assumptions is wrong

Hence , 2 + √3 is a irrational number