Question

prove that 3+2√5 is an irrational number

Answer 1

I hope this helps you

Answer 2

let us assume
$3 + 2 \sqrt{5}$
is a rational
i.e
$3 + 2 \sqrt{5}$
is rational
hence,
$3 + 2 \sqrt{5}$
can be written in form of p/q
where a and b(b is not equal to 0)are co prime.
hence,
$3 + 2 \sqrt{5 } = \frac{a}{b}$
$2 \sqrt{5} = \frac{a}{b} - 3$
$2 \sqrt{5} = \frac{a - 3b}{b}$
$\sqrt{5} = \frac{1}{2} \times \frac{a - 3b}{b}$
$\sqrt{5} = \frac{a - 3b}{2b}$
next is in picture above