Question

2√3+√5 prove that is irrational

Answer 1

may it will help you

Answer 2

let m= 2√3+√5 be rational,if possible.
m-√5=2√3
m-√5/2 =√3

let if possible√3 be rational number
let √3=a/b where g.c.d(a,b) =1
${a}^{2} = 3 {b}^{2}$

3|a^2
3|a
let
$a = 3 {a1}$
$9{a1}^{2} = {a}^{2} = {b}^{2}$
${b}^{2} = 3{a1}^{2}$
3|b^2
3|b

3|a and 3|b
but g.c.d (a,b)=1
we come to contradiction
√3 is irrational
$\frac{m - \sqrt{5} }{2} = \sqrt{3}$
so,2√3+√5 is irrational