Question

prove that √2+5√5 is irrational.​

Answer 1

let given number is rational

then we can

say that..

√2+5√5=p/q..(squaring both sides)

2+125+10√10=p^2/q^2

10√10=p^2/q^2-127 (rational)

if we move 10 to RHS

Then we can say that √10 is clearly irrational.

But RHS Part rational

rational number not is equal to rational

Hence we can say the number is irrational.(by contrary method)