Question

Show that (√3+√5)square is an irrational

Answer 1

let (√3+√5) be a rational no
so √3+√5 = p/q where p and q are intezers and q is not equal to zero

(√3+√5) = p/q

Squaring both side

(√3+√5)^2= (p/q)^2
3+5+2√8 = (p/q) ^2
8+2√8 = (p/q)^2

In the LHS we can observe that it is irrational no
In the RHS we can observe that it is rational no
Irrational can never be equal to rational no
This contradiction has arisen due to our wrong assumption that (√3+√5) is rational no

So (√3+√5) is a irrational no