Question

prove that √3+2√5 is an irrational

Answer 1

let √3+2√5 is rational,so it can represented in the form of a/b

$2 \sqrt{5} = \frac{a}{b} \\ \sqrt{5} = \frac{a}{2b}$
we know that √5 is irrational number it cannot be represented in the form of a/b,si from the conflict we can say that 2√5 is irrational.
√3 is irrational too.
and addition of these two numbers is irrational number