Question

√7 +2 is rational/irrational number??​

Answer 1

$\underline{\underline{\huge{\pink{\tt{\textbf Answer :-}}}}}$

Let us assume that 7+√2 is a rational number

Then. there exist coprime integers , p, q,such that q≠0 such that

$7 + \sqrt{2} = \frac{p}{q}$

$\sqrt{2} = \frac{p}{q} - 7$

Here,p/q-7 is a rational number, but √2 is a irrational number. But, a irrational cannot be equal to a rational number.

This is a contradiction.

Thus, our assumption is wrong.

Therefore 7+√2 is a irrational number.