Question

Prove that (2+√3) is irrational

Answer 1

here is your answer in the above pick and please follow me and mark it as brain liest

Answer 2

$\large\underline\mathrm\red{Given:-}$

• 2 + √3

$\large\underline\mathrm\red{To \: find}$

• Prove that 2 + √3 is Irrational.

$\large\underline\mathrm\red{Solution}$

• Let us assume, to the contrary, that 2 + √3 is a rational number, it can be written in the form of p/q where, q ≠ 0

»★ p  and  q  are  coprimes

⟹ 2 + √3 = p/q

⟹ √3 = p/q - 2

⟹ √3 = p - 2q / q

$\large\underline\mathrm\red{Since, \: p \: and \: q \: are \: integers}$

⟹ p - 2q / q is a rational number.

≫ therefore √3 is a rational number

»»But √3 is an irrational number.

$\large\underline\mathrm\red{This \: shows \: our \: assumption \: is \: incorrect.}$

❝So, we conclude that 2 + √3 is not a rational number.❞

✰Hence, 2 + √3 is an irrational number.

______________________________________