Question

Solve
2√3+√5 is an irrational

Answer 1

hope it is helpful for you

Answer 2

let us suppose that 2√3+√5 is rational
∴2√3+√5=x,which is rational
2√3=x-√5
√3=x-√5/2
3=(x-√5)²/2²
3=x²+(√5)²-2√5x/4
3=x²+5-2√5x/4
multiply the whole equation with 4
⇒12=x²+5-2√5x
subtract 5 from LHS and RHS
⇒7=x²-2√5x
-2√5x=7-x²
√5=7-x²/-2x
since x is rational rhs is also rational
⇒LHS=√5 is also rational
this contradicts the fact that √5 is irrational
∴our supposition that 2√3+√5 is rational is wrong
∴2√3+√5 is irrational

Hope this will help you