Question

prove 3+2√5 is irrational​

Answer 1

$\huge\mathfrak\color {red}AnSwEr$

$\sf\blue {\underline {\sf ☆Let,}}$

$3+2\sqrt {3}$ be a rational number.

Here, p and q are co-primes & q isn't equal to 0.

$\sf\orange {\underline {\sf ☆Since,}}$

$2 \sqrt{5} = \frac{p}{q} - 3$

$2 \sqrt{{5} } = \frac{p - 3q}{q}$

$\sqrt{5} = \frac{p - 3q}{2q}$

It contradicts, the fact that $3+2\sqrt {5}$ is rational number.

$\sf\purple {\underline {\sf ☆But,}}$

this contradiction arised because of our wrong assumption that $3+2\sqrt {5}$ is rational number.

$\huge\green {Hence,}$

$3+2\sqrt {5}$ is irrational number.